reductions of minimal lagrangian submanifolds with symmetries let m be a fano manifold equipped with a kahler form omega in 2 pi c 1 m and k a connected compact lie group acting on m as holomorphic isometries in this paper we show the minimality of a k invariant lagrangian submanifold l in m with respect to a globally conformal kahler metric is equivalent to the minimality of the reduced lagrangian submanifold l 0 l k in a kahler quotient m 0 with respect to the hsiang lawson metric furthermore we give some examples of kahler reductions by using a circle action obtained from a cohomogenenity one action on a kahler einstein manifold of positive ricci curvature applying these results we obtain several examples of minimal lagrangian submanifolds via reductions

comparison results and estimates on the gradient without strict convexity in this paper we establish a comparison result for solutions to the problem mbox minimize int omega f nabla u x dx quad hbox on u u u 0 in w 1 1 0 omega

lipschitz regularity for minima without strict convexity of the lagrangian abstract we give in a non smooth setting some conditions under which some of the minimizers of f u x d x g x u x d x among the functions in w 1 1 that lie between two lipschitz functions are lipschitz we weaken the usual strict convexity assumption in showing that if just the faces of the epigraph of a convex function f r n r are bounded and the boundary datum u 0 satisfies a generalization of the bounded slope condition introduced by a cellina then the minima of f u x d x on u 0 w 0 1 1 whenever they exist are lipschitz a relaxation result follows

nonlinear response of composite panels under combined acoustic excitation and aerodynamic pressure a e nite element formulation is presented for the analysis of the large dee ection response of composite panels subjected to high acoustic excitation and aerodynamic pressure at supersonic e ow the e rst order shear defor mation theory is considered for laminated composite plates and the von karm an nonlinear strain displacement relations are employed for panel large dee ection response the e rst order piston theory aerodynamics and the simulated gaussian white noise are employed for the aerodynamic and acoustic loads respectively the nonlinear equationsofmotion foranarbitrarily laminated compositepanelsubjectedto combined aerodynamicand acoustic pressures are formulated e rst in structure node degrees of freedom the system equations are then transformed and reduced to a set of coupled nonlinear equations in modal coordinates modal participation is dee ned and the in vacuo modes to be retained in the analysis are based on the modal participation values numerical results include root mean square values of maximum dee ections dee ection and strain response time histories probability distributions power spectrum densities and skewness and kurtosis results showed that combined acoustic and aerodynamic loads have to be considered for panel analysis and design at high dynamic pressure values

flutter of geometrically imperfect shear deformable laminated flat panels using non linear aerodynamics abstract the dynamic instability resulting from a high supersonic flow over a simply supported laminated flat panel subjected to uniform in plane edge compression is studied the structural model incorporates geometrical non linearities transverse shear deformation and transverse normal stress effects and satisfies the traction free condition on both faces of the panel in plane edge restraints and small initial geometric imperfections are also considered aerodynamic loads based on the third order piston theory are used and the panel flutter equations are derived via galerkin s method the arclength continuation method is used to determine the static equilibrium state whose dynamic stability behavior is subsequently examined the effects of transverse shear flexibility aerodynamic non linearities initial imperfections and in plane plate theory generally overpredicts the critical flow speed and compressive load and a shear deformation theory is required when considering panels that are flexible in transverse shear when aerodynamic non linearities are included multiple flutter speeds may exist the nature of the flutter boundary for perfect panels is determined by the method of multiple scales and it is seen that the presence of aerodynamic non linearities could result in the hard flutter phenomenon results indicate that non linear aerodynamics is important for panels that are not sufficiently thin i e panels characterized by a high flutter mach number

on lagrangian submanifolds in complex hyperquadrics and isoparametric hypersurfaces in spheres the n dimensional complex hyperquadric is a compact complex algebraic hypersurface defined by the quadratic equation in the n 1 dimensional complex projective space which is isometric to the real grassmann manifold of oriented 2 planes and is a compact hermitian symmetric space of rank 2 in this paper we study geometry of compact lagrangian submanifolds in complex hyperquadrics from the viewpoint of the theory of isoparametric hypersurfaces in spheres from this viewpoint we provide a classification theorem of compact homogeneous lagrangian submanifolds in complex hyperquadrics by using the moment map technique moreover we determine the hamiltonian stability of compact minimal lagrangian submanifolds embedded in complex hyperquadrics which are obtained as gauss images of isoparametric hypersurfaces in spheres with g 1 2 3 distinct principal curvatures

a connectedness property of algebraic moment maps let k be a connected compact lie group and m a hamiltonian k manifold i e a symplectic k manifold equipped with a moment map m k liek a theorem of kirwan implicitly in ki asserts if m is connected and compact then the level sets of are connected the purpose of this note is to prove such a statement in the category of algebraic varieties first we reformulate kirwan s theorem consider the map m k k which is the composition of with the quotient map for a point x k let h kx be its isotropy group and y kx k k its orbit then the fiber y is isomorphic to the fiber product k x thus since both k h and h are connected the connectedness of the fibers of is equivalent to the connectedness of the fibers of this formulation is more suitable for the algebraic category let g be a connected reductive group everything over c and z a hamiltonian gvariety with moment map z g lieg let g g specc g be the categorical quotient and let z g g be the composition of with the quotient map since the latter is not an orbit map the connection between fibers of and is much more loose than in the differential category and we concentrate on from now on the morphism is still not the right map since sometimes not even its generic fibers are connected an example is the action of g sl2 c on z c 2 c this is the cotangent bundle of c then g g a and u u in particular the generic fiber of has two connected components this is remedied by looking at the map u u instead then is the composition of with the finite map a a z 7 z the latter being responsible for the disconnected fibers this construction can be generalized as follows the morphism induces an homomorphism of algebras

second variation and stabilities of minimal lagrangian submanifolds in kahler manifolds first we derive a new second variation formula which holds for any minimal lagrangian submanifold in k ihler manifolds using this we prove that any minimal lagrangian submanifold in kfihler manifolds with nonpositive chern class is stable we also prove that in kfihler manifolds with positive chern class any stable minimal lagrangian submanifold l satisfies that h l 0 next we introduce the notion of hamiltonian stability either local or global of minimal lagrangian submanifolds in einstein kfihler manifolds using our second variation formula we find a general criterion for the local hamiltonian stability for minimal lagrangian submanifolds in einstein k ihler manifolds this criterion is satisfied for all real forms which are einstein of irreducible hermitian symmetric spaces e g the cannonical rp c cp it is also satisfied by the clifford torus t c cp

symplectic surgery and the spinc dirac operator abstract letgbe a compact connected lie group and m a compact hamiltoniang space with moment mapj m g under the assumption that these data are pre quantizable one can construct an associated spinc dirac operator formula whose equivariant index yields a virtual representation ofg we prove a conjecture of guillemin and sternberg that if 0 is a regular value ofj the multiplicityn 0 of the trivial representation in the index space formula is equal to the index of the spinc dirac operator for the symplectic quotientm0 j 1 0 g this generalizes previous results for the case thatg tis abelian i e a torus

proper orthogonal decomposition method for analysis of nonlinear panel flutter with thermal effects in supersonic flow abstract the proper orthogonal decomposition pod method for analysis of nonlinear panel flutter subjected to supersonic flow is presented optimal pod modes are extracted from a chaotic galerkin mode responses the aeroelastic equations of motion are constructed using von karman plate theory first order piston theory and quasi steady thermal stress theory a simply supported plate with thermal loads from a uniformly distributed temperature is considered many types of panel behaviors including stable flat dynamically stable buckled limit cycle oscillation nonharmonic periodic motion quasi periodic motion and chaotic motion are observed our primary focus is on chaos and the route to chaos it is found that a sudden transition from the buckled state to chaos occurs time history phase portrait poincare map bifurcation diagram and lyapunov exponent are employed to study chaos the pod chaotic results obtained are compared with the traditional galerkin solutions it is shown that the pod method can obtain accurate chaotic solutions using fewer modes and less computational effort than the galerkin mode approach additionally the pod method converges faster in the analysis of chaotic transients effects of length to width ratios and thermal loads are presented it is found that a smaller width for fixed length will produce more stable flutter response while the thermal loads degrade the flutter boundary and result in a more complex evolution of dynamic motions the numerical simulations show that the robustness of the pod modes depends on the dynamic pressure but not on temperature

convex bodies of states and maps we give a general solution to the question of when the convex hulls of orbits of quantum states on a finite dimensional hilbert space under unitary actions of a compact group have a non empty interior in the surrounding space of all density operators the same approach can be applied to study convex combinations of quantum channels the importance of both problems stems from the fact that usually only sets with non vanishing volumes in the embedding spaces of all states or channels are of practical importance for the group of local transformations on a bipartite system we characterize maximally entangled states by the properties of a convex hull of orbits through them we also compare two partial characteristics of convex bodies in terms of the largest balls and maximum volume ellipsoids contained in them and show that in general they do not coincide separable states mixed unitary channels and k entangled states are also considered as examples of our techniques

continuity properties of solutions to some degenerate elliptic equations abstract we consider a nonlinear possibly degenerate elliptic operator l v div a v b x v where the field a and the function b are unnecessarily strictly monotonic and a satisfies a very mild ellipticity assumption for a given boundary datum we prove the existence of the maximum and the minimum of the solutions and formulate a haar rado type result namely a continuity property for these solutions that may follow from the continuity of in the homogeneous case we formulate some generalizations of the bounded slope condition and use them to obtain the lipschitz or local lipschitz regularity of solutions to l u 0 we prove the global holder regularity of the solutions in the case where is lipschitz

the spectrum of a hermitian matrix sum abstract an announcement by lidskii b v lidskii functional anal appl 10 1982 76 77 russian 139 140 english claimed to establish the explicit description of the spectrum of a hermitian matrix sum in the form conjectured by horn a horn pacific j math 16 1962 225 241 but no supporting proof has been published this paper begins an analysis of the claim and is the first step towards bridging the distance between the elementary methods of horn s 1962 paper and the partial solution of the same problem using noncommutative harmonic analysis by dooley et al i dooley r repka n wildberger lin mult alg 36 1993 79 102 the methods of horn lidskii lead to combinatorial issues of independent interest

on the bounded slope condition and the validity of the euler lagrange equation under the bounded slope condition on the boundary values of a minimization problem for a functional of the gradient of u we show that a continuous minimizer w is in fact lipschitzian an application of this result to prove the validity of the euler lagrange equation for w is presented

how many invariant polynomials are needed to decide local unitary equivalence of qubit states given l qubit states with the fixed spectra of reduced one qubit density matrices we find a formula for the minimal number of invariant polynomials needed for solving local unitary lu equivalence problem that is problem of deciding if two states can be connected by local unitary operations interestingly this number is not the same for every collection of the spectra some spectra require less polynomials to solve lu equivalence problem than others the result is obtained using geometric methods i e by calculating the dimensions of reduced spaces stemming from the symplectic reduction procedure

kirillov s orbit method the case of discrete series representations let be a discrete series representation of a real reductive lie group g and let g be a reductive subgroup of g in this paper we give a geometric expression of the g multiplicities in g when the representation is g admissible

convexity and unitary representations of nilpotent lie groups the moment map of symplectic geometry is extended to associate to any unitary representation of a nilpotent lie group ag invariant subset of the dual of the lie algebra we prove that this subset is the closed conex hull of the kirillov orbit of the representation

openness and convexity for momentum maps the purpose of this paper is finding the essential attributes underlying the convexity theorems for momentum maps it is shown that they are of a topological nature more specifically we show that convexity follows if the map is open onto its image and has the so called local convexity data property these conditions are satisfied in all the classical convexity theorems and hence they can in principle be obtained as corollaries of a more general theorem that has only these two hypotheses we also prove a generalization of the so called local to global principle that only requires the map to be closed and to have a normal topological space as domain instead of using a properness condition this allows us to generalize the flaschka ratiu convexity theorem to noncompact manifolds

hamiltonian stability of the gauss images of homogeneous isoparametric hypersurfaces i the image of the gauss map of any oriented isopara metric hypersurface of the unit standard sphere s n 1 1 is a mini mal lagrangian submanifold in the complex hyperquadric qn c in this paper we determine the hamiltonian stability of all com pact minimal lagrangian submanifolds embedded in complex hy perquadrics which are obtained as the images of the gauss map of homogeneous isoparametric hypersurfaces in the unit spheres

eigenvalue distributions of reduced density matrices given a random quantum state of multiple distinguishable or indistinguishable particles we provide an effective method rooted in symplectic geometry to compute the joint probability distribution of the eigenvalues of its one body reduced density matrices as a corollary by taking the distribution s support which is a convex moment polytope we recover a complete solution to the one body quantum marginal problem we obtain the probability distribution by reducing to the corresponding distribution of diagonal entries i e to the quantitative version of a classical marginal problem which is then determined algorithmically this reduction applies more generally to symplectic geometry relating invariant measures for the coadjoint action of a compact lie group to their projections onto a cartan subalgebra and can also be quantized to provide an efficient algorithm for computing bounded height kronecker and plethysm coefficients

non linear vibrations of laminated cylindrical shallow shells under thermomechanical loading abstract the geometrically non linear vibrations of linear elastic composite laminated shallow shells under the simultaneous action of thermal fields and mechanical excitations are analysed for this purpose a model based on a very efficient p version first order shear deformation finite element with hierarchical basis functions is employed the equations of motion are solved in the time domain by a newmark implicit time integration method the model and code developed are partially validated by comparison with published data parametric studies are carried out in order to study the influence of temperature change initial curvature panel thickness and fibre orientation on the shells dynamics

localization of the riemann roch character abstract we present a k theoretic approach to the guillemin sternberg conjecture v guillemin and s sternberg invent math 67 1982 515 538 about the commutativity of geometric quantization and symplectic reduction which was proved by e meinrenken j amer math soc 9 1996 373 389 adv math 134 1998 240 277 and tian zhang y tian and w zhang invent math 132 1998 229 259 besides providing a new proof of this conjecture for the full non abelian group action case our methods lead to a generalization for compact lie group actions on manifolds that are not symplectic these manifolds carry an invariant almost complex structure and an abstract moment map

stacking sequence design of flat composite panel for flutter and thermal buckling in this paper we formulate the stacking sequence design of laminated composite flat panels for maximum supersonic flutter speed and maximum thermal buckling capacity the design is constrained to have stable limit cycle oscillation in the vicinity of the flutter boundary for the purpose of comparison we consider both linear and nonlinear panel flutter analyses because of manufacturing constraints the stacking sequence of the laminate is selected from a discrete set of orientation angles the plate is modeled using von karman plate equations and assumed to be subjected to uniform temperature differential the aerodynamic load on the plate is computed using third order piston theory the plate equations of motion are derived using hamilton s principle and discretized using the rayleigh ritz method the nonlinear panel flutter analysis is performed using an approximate perturbation approach the pareto fronts describing the trade off between thermal buckling and flutter are generated for different panel aspect ratios it is observed that optimal designs obtained for both linear and nonlinear flutter analyses are similar with only the predicted flutter speeds different this suggests that for the purpose of preliminary stacking sequence design linear flutter analysis is sufficient

semitoric integrable systems on symplectic 4 manifolds let m be a symplectic 4 manifold a semitoric integrable system on m is a pair of smooth functions j h c m r for which j generates a hamiltonian s 1 action and the poisson brackets j h vanish we shall introduce new global symplec tic invariants for these systems some of these invariants encode topological or geometric aspects while others encode analytical information about the singularities and how they stand with respect to the system our goal is to prove that a semitoric system is completely determined by the invariants we introduce

convex analysis on cartan subspaces in 1937 von neumann 31 gave a famous characterization of unitarily invariant matrix norms that is norms f on cp q satisfying f uxv f x for all unitary matrices u and v and matrices x in cp q his result states that such norms are those functions of the form g where the map x cp q 7 x r has components the singular values 1 x 2 x p x of x assuming p q and g is a norm on rp invariant under sign changes and permutations of components furthermore he showed the respective dual norms satisfy

connections of berry and hannay type for moving lagrangian submanifolds abstract berry s phase is the holonomy of the natural connection on the canonical circle bundle over projectivized quantum hilbert space given a symplectic manifold p a classical limit of this phase is constructed as the holonomy of a berry connection over a finite codimensional isodrastic foliation defined by constancy of action integrals on the space of lagrangian submanifolds in p equipped with smooth densities of total measure 1 if the densities are determined by a kahler metric compatible with the symplectic structure the curvature of the berry connection at the lagrangian submanifold l is given by a simple formula involving curvature of l in particular the berry connection defines a homotopy invariant for isodrastic loops of minimal lagrangian submanifolds in a simply connected kahler manifold a similar invariant constructed by the author for loops of symplectomorphisms is also a special case of the classical berry phase a classical analogue of berry s phase was discovered by hannay for moving families of completely integrable systems following berry and hannay we interpret hannay s angles as the holonomy of a hannay connection on a bundle of tori over the isodrastic foliation on the space of lagrangian toral layers consisting of lagrangian tori with a flat affine structure and an extension of this structure to the first infinitesimal neighborhood finally we show that the hannay angles are the derivatives with respect to action variables of the classical berry phase

the first eigenvalue of the laplacian of an isoparametric minimal hypersurface in a unit sphere soit m n 1 une variete de riemann connexe compacte a n 1 dimensions sans bord et son laplacien agissant sur des fonctions lisses sur m a un spectre discret 0 0 m 1 m 2 m k m x soit f une immersion minimale de m n 1 dans la sphere unite a n dimensions s n 1 de l espace euclidien on etudie la premiere valeur propre du laplacien d une hypersurface isoparametrique minimale fermee dans s n 1

decomposable representations and lagrangian submanifolds of moduli spaces associated to surface groups the importance of explicit examples of lagrangian submanifolds of moduli spaces is revealed by papers such as dostoglou and salamon ann of math 2 139 3 581 640 1994 and salamon proceedings of the international congress of mathematicians vol 1 2 zurich 1994 pp 526 536 birkhauser basel 1995 given a 3 manifold m with boundary m dostoglou and salamon use such examples to obtain a proof of the atiyah floer conjecture relating the symplectic floer homology of the representation space hom 1 m u u associated to an explicit pair of lagrangian submanifolds of this representation space and the instanton homology of the 3 manifold m in the present paper we construct a lagrangian submanifold of the space of representations mathcal m g l hom mathcal c pi g l u u of the fundamental group g lof a punctured riemann surface g l into an arbitrary compact connected lie group u this lagrangian submanifold is obtained as the fixed point set of an anti symplectic involution hat beta defined on mathcal m g l we show that the involution hat beta is induced by a form reversing involution defined on the quasi hamiltonian space u times u g times mathcal c 1 times cdots times mathcal c l the fact that hat beta has a non empty fixed point set is a consequence of the real convexity theorem for group valued momentum maps proved in schaffhauser a real convexity theorem for quasi hamiltonian actions submitted 25 p 2007 http arxiv org abs math 0705 0858 the notion of decomposable representation provides a geometric interpretation of the lagrangian submanifold thus obtained

convexity properties of gradient maps abstract we consider the action of a real reductive group g on a kahler manifold z which is the restriction of a holomorphic action of a complex reductive group h we assume that the action of a maximal compact subgroup u of h is hamiltonian and that g is compatible with a cartan decomposition of h we have an associated gradient map p z p where g k p is the cartan decomposition of g for a g stable subset y of z we consider convexity properties of the intersection of p y with a closed weyl chamber in a maximal abelian subspace a of p our main result is a convexity theorem for real semi algebraic subsets y of z p v where v is a unitary representation of u

automorphisms of multiplicity free hamiltonian manifolds let m be a multiplicity free hamiltonian manifold m for a connected compact lie group k not necessarily abelian let p be the momentum polytope of m we calculate the automorphism of m as a sheaf over p and show that all higher cohomology groups of this sheaf vanish from this and a recent theorem of losev we deduce a conjecture of delzant the momentum polytope and the principal isotropy group determine m up to isomorphism moreover we give a criterion for when a polytope and a group are afforded by a multiplicity free manifold

the lack of strict convexity and the validity of the comparison principle for a simple class of minimizers abstract let w x a x b be an affine function in r n r n l r n r be convex and w be a local minimizer of i v l v x d x in w 1 1 r with w x w x on in the trace sense then w satisfies the comparison principle from above i e w x w x a e on if and only if a l a does not belong to the relative interior of a n dimensional face of the epigraph of l as a consequence if f is the projection of a bounded face of the epigraph of l the local minimizer w x max x x 0 f satisfies the comparison principle from above if and only if dim f n 1 or x 0

nonlinear flutter of composite panels under yawed supersonic flow using finite elements a finite element formulation is presented for the effects of arbitrary flow direction on the large amplitude supersonic flutter of composite panels the von karman large deflection plate theory is used to account for large amplitude limit cyde oscillations quasisteady first order piston theory aerodynamics is employed for aerodynamic loading and first order shear deformation theory is used for laminated composite panels an efficient solution procedure is presented by using the modal transformation to reduce the number of nonlinear panel flutter equations and then applying the linearized updated mode with nonlinear time function approximation to the reduced nonlinear panel flutter modal equations a modal participation is defined and the minimum number of linear modes for accurate and converged limit cycle response can be ensured examples are given for isotropic and composite panels at yawed supersonic flow

isoparametric hypersurfaces with four principal curvatures let m be an isoparametric hypersurface in the sphere s n with four distinct principal curvatures munzner showed that the four principal curvatures can have at most two distinct multiplicities m1 m 2 and stolz showed that the pair m1 m 2 must either be 2 2 4 5 or be equal to the multiplicities of an isoparametric hypersurface of fkm type constructed by ferus karcher and munzner from orthogonal representations of clifford algebras in this paper we prove that if the multiplicities satisfy m2 2m1 1 then the isoparametric hypersurface m must be of fkm type together with known results of takagi for the case m1 1 and ozeki and takeuchi for m1 2 this handles all possible pairs of multiplicities except for four cases for which the classification problem remains open

a construction of new families of minimal lagrangian submanifolds via torus actions in this paper we investigate connections between minimal lagrangian submanifolds and holomorphic vector fields in kahler manifolds our main result is let m2n n 2 be a kahler einstein manifold with positive scalar curvature with an effective structure preserving action by an n torus tn then precisely one regular orbit l of the tn action is a minimal lagrangian submanifold of m moreover there is an n 1 torus tn 1 tn and a sequence of non flat immersed minimal lagrangian tori lk in m such that all lk are invariant under tn 1 and lk locally converge to l in particular the supremum of the sectional curvatures of lk and the distance between l and lk go to 0 as k this result is new even for m pn for n 3

finite element modal formulation for hypersonic panel flutter analysis with thermal effects a finite element time domain modal formulation for analyzing nonlinear flutter of panels subjected to hypersonic airflow has been developed von karman large deflection plate theory is used for description of the structural nonlinearity and third order piston theory is employed to consider the aerodynamic nonlinearity the thermal loadings of uniformly distributed surface temperatures and temperature gradients through the panel thickness are considered by the application of the modal truncation technique the number of governing equations of motion is reduced dramatically so that the computational costs are reduced significantly all possible types of panel behavior including flat and stable buckled but dynamically stable limit cycle oscillation lco periodic motion and chaotic motion were observed examples of the applications of the proposed methodology were flutter responses of isotropic and composite panels special emphasis was placed on the boundary between lco and chaos and on the route to chaos time history phase plane plot poincare map bifurcation diagram and lyapunov exponent are employed in the chaos study it is found that at low or moderately high dynamic pressures the fluttering panel typically takes a period doubling route to evolve into chaos whereas at high dynamic pressures the route generally involves bursts of chaos and rejuvenations of periodic motions

finite element time domain modal formulation for nonlinear flutter of composite panels a finite element time domain modal approach is presented for determining the nonlinear flutter characteristics of composite panels at elevated temperatures the von karman large deflection strain displacement relations quasisteady first order piston theory aerodynamics and quasisteady thermal stress theory are used to formulate the nonlinear panel flutter finite element equations of motion in nodal displacements a set of nonlinear modal equations of motion of much smaller degrees of freedom for the facilitation in time numerical integration is then obtained through a modal transformation and reduction all five types of panel behavior flat buckled limit cycle periodic and chaotic motions can be determined

convexity properties of the moment mapping re examined abstract consider a hamiltonian action of a compact lie group on a compact symplectic manifold a theorem of kirwan s says that the image of the momentum mapping intersects the positive weyl chamber in a convex polytope i present a new proof of kirwan s theorem which gives explicit information on how the vertices of the polytope come about and on how the shape of the polytope near any point can be read off from infinitesimal data on the manifold it also applies to some interesting classes of noncompact or singular hamiltonian spaces such as cotangent bundles and complex affine varieties

on distinguished orbits of reductive representations abstract let g be a real reductive lie group and let g gl v be a real reductive representation of g with restricted moment map m g v 0 g in this work we introduce the notion of nice space of a real reductive representation to study the problem of how to determine if a g orbit is distinguished i e it contains a critical point of the norm squared of m g we give an elementary proof of the well known convexity theorem of atiyah guillemin sternberg in our particular case and we use it to give an easy to check sufficient condition for a g orbit of an element in a nice space to be distinguished in the case where g is algebraic and is a rational representation the above condition is also necessary making heavy use of recent results of michael jablonski obtaining a generalization of nikolayevsky s nice basis criterion we also provide useful characterizations of nice spaces in terms of the weights of finally some applications to ternary forms are presented

polar and coisotropic actions on kahler manifolds the main result of the paper is that a polar action on a compact irreducible homogeneous kahler manifold is coisotropic this is then used to give new examples of polar actions and to classify coisotropic and polar actions on quadrics

sums of adjoint orbits and l2 singular dichotomy for su m abstract let g be a real compact connected simple lie group and g its lie algebra we study the problem of determining from root data when a sum of adjoint orbits in g or a product of conjugacy classes in g contains an open set our general methods allow us to determine exactly which sums of adjoint orbits in su m and products of conjugacy classes in su m contain an open set in terms of the highest multiplicities of eigenvalues for su m and su m we show l 2 singular dichotomy the convolution of invariant measures on adjoint orbits or conjugacy classes is either singular to haar measure or in l 2

spin c geometry of kahler manifolds and the hodge laplacian on minimal lagrangian submanifolds from the existence of parallel spinor fields on calabi yau hyper kahler or complex flat manifolds we deduce the existence of harmonic differential forms of different degrees on their minimal lagrangian submanifolds in particular when the submanifolds are compact we obtain sharp estimates on their betti numbers which generalize those obtained by smoczyk in 49 when the ambient manifold is kahler einstein with positive scalar curvature and especially if it is a complex contact manifold or the complex projective space we prove the existence of kahlerian killing spinor fields for some particular spin c structures using these fields we construct eigenforms for the hodge laplacian on certain minimal lagrangian submanifolds and give some estimates for their spectra these results also generalize some theorems by smoczyk in 50 finally applications on the morse index of minimal lagrangian submanifolds are obtained

convexity properties of the moment mapping ii be its associated momen t mapping see w for definitions the set x is the union of co adjoint orbits the main result of this paper is a description of the orbit structure of this set to describe this result we first note that the coadjoint orbits in q can be parametr ized as follows let t be a caf tan subalgebra of g and let b be a positive definite g invariant bilinear form on by means of b we get a g equivariant identification q let t be the subspace of q corresponding to t then every co adjoint orbit intersects i in a weyl group orbit so there is a one one correspondence between co adjoint orbits in q and weyl group orbits in t to get an even sharper parametrization let t be a weyl chamber in then every weyl group orbit intersects t in a single point so t is a modul i space for the co adjoint orbits two orbits in x are said to be of the same type if they are isomorphic as homogeneous g spaces since x is compact there are at most a finite number of different types of orbits see 1113 let h be a closed subgroup of t of codimension r and let cit be the set of all orbits in x of type g h

an analytic proof of the geometric quantization conjecture of guillemin sternberg we present a direct analytic approach to the guillemin sternberg conjecture gs that geometric quantization commutes with symplectic reduction which was proved recently by meinrenken m1 m2 and vergne v1 v2 et al besides providing a new proof of this conjecture our methods also lead immediately to further extensions in various contexts

when is a pure state of three qubits determined by its single particle reduced density matrices using techniques from symplectic geometry we prove that a pure state of three qubits is up to local unitaries uniquely determined by its one particle reduced density matrices exactly when their ordered spectra belong to the boundary of the so called kirwan polytope otherwise the states with given reduced density matrices are parameterized up to local unitary equivalence by two real variables given inevitable experimental imprecision this means that already for three qubits a pure quantum state can never be reconstructed from single particle tomography we moreover show that the knowledge of the reduced density matrices is always sufficient if one is given the additional promise that the quantum state is not convertible to the greenberger horne zeilinger state by stochastic local operations and classical communication and discuss generalizations of our results to an arbitrary number of qubits

kahlerian potentials and convexity properties of the moment map since kostant proved his convexity theorems for torus actions on ag varieties ko there have been numerous contributions to this subject in the more general symplectic and k ahlerian setting for example let k be a compact lie group acting in a hamiltonian fashion on a connected compact symplectic manifold x then the intersection x of the image of the moment map x liek with a positive weyl chamber t is convex thus x k x where x is a natural convex section this was proved by atiyah and guillemin sternberg a g s in the abelian case i e where k t is a compact torus by mumford m for x projective algebraic with an integral k ahlerian structure and k not necessarily abelian and in its nal form in the compact symplectic case by kirwan k a precise description of x x t in the compact k ahlerian framework can be given in terms of the image of the components of the set of t xed points in x in the projective case where the k ahlerian structure comes from a projective embedding there are explicit connections to the representations theory of g kc which are due to brion and to mumford ness b n the purpose of the present paper is to prove convexity properties of in the setting of non compact k ahlerian spaces note that by removing an appropriate k invariant subset from x one can easily construct non convex images from convex ones on the other hand hilgert neeb plank proved h n p that convexity holds for a proper moment map x liek another convexity result has been obtained by sjamaar for x a ne and the restriction of the moment map of a representation s2 here the representation theoretical approach of brion is used now let x be an irreducible complex space endowed with a holomorphic action of a complex reductive group g assume that a maximal

the convexity package for hamiltonian actions on conformal symplectic manifolds consider a hamiltonian action of a compact connected lie group on a conformal symplectic manifold we prove a convexity theorem for the moment map under the assumption that the action is of lee type which establishes an analog of kirwan s convexity theorem in conformal symplectic geometry

algebraic hamiltonian actions in this paper we deal with a hamiltonian action of a reductive algebraic group g on an irreducible normal affine poisson variety x we study the quotient morphism mu g x g x g rightarrow mathfrak g g of the moment map mu g x x rightarrow mathfrak g we prove that for a wide class of hamiltonian actions including for example actions on generically symplectic varieties all fibers of the morphism g x g have the same dimension we also study the stein factorization of g x g namely let c g x denote the spectrum of the integral closure of mu g x mathbb k mathfrak g g in mathbb k x g we investigate the structure of the mathfrak g g scheme c g x our results partially generalize those obtained by f knop for the actions on cotangent bundles and symplectic vector spaces

determining lyapunov exponents from a time series we present the first algorithms that allow the estimation of non negative lyapunov exponents from an experimental time series lyapunov exponents which provide a qualitative and quantitative characterization of dynamical behavior are related to the exponentially fast divergence or convergence of nearby orbits in phase space a system with one or more positive lyapunov exponents is defined to be chaotic our method is rooted conceptually in a previously developed technique that could only be applied to analytically defined model systems we monitor the long term growth rate of small volume elements in an attractor the method is tested on model systems with known lyapunov spectra and applied to data for the belousov zhabotinskii reaction and couette taylor flow

angular momenta of relative equilibrium motions and real moment map geometry chenciner and jimenez perez mosc math j 13 4 621 630 2013 showed that the range of the spectra of the angular momenta of all the rigid motions of a fixed central configuration in a general euclidean space form a convex polytope in this note we explain how this result follows from a general convexity theorem of o shea and sjamaar in real moment map geometry math ann 31 415 457 2000 finally we provide a representation theoretic description of the pushforward of the normalized measure under the real moment map for riemannian symmetric pairs