on the l r hodge theory in complete non compact riemannian manifolds we study solutions for the hodge laplace equation delta u omega on p forms with displaystyle l r estimates for displaystyle r 1 our main hypothesis is that delta has a spectral gap in displaystyle l 2 we use this to get sl non classical displaystyle l r hodge decomposition theorems an interesting feature is that to prove these decompositions we never use the boundedness of the riesz transforms in displaystyle l s par these results are based on a generalisation of the raising steps method to complete non compact riemannian manifolds

finite group extensions and the atiyah conjecture the atiyah conjecture for a discrete group g states that the l 2 betti numbers of a finite cw complex with fundamental group g are integers if g is torsion free and in general that they are rational numbers with denominators determined by the finite subgroups of g here we establish conditions under which the atiyah conjecture for a torsion free group g implies the atiyah conjecture for every finite extension of g the most important requirement is that h g z p is isomorphic to the cohomology of the p adic completion of g for every prime p an additional assumption is necessary e g that the quotients of the lower central series or of the derived series are torsion free we prove that these conditions are fulfilled for a certain class of groups which contains in particular artin s pure braid groups and more generally fundamental groups of fiber type arrangements free groups fundamental groups of orientable compact surfaces certain knot and link groups primitive positive one relator groups and products of these therefore every finite in fact every elementary amenable extension of these groups satisfies the atiyah conjecture as a consequence if such an extension h is torsion free then the group ring ch contains no non trivial zero divisors i e h fulfills the zero divisor conjecture in the course of the proof we prove that if these extensions are torsionfree then they have plenty of non trivial torsion free quotients which are virtually nilpotent all of this applies in particular to artin s full braid group therefore answering question b6 on www grouptheory org our methods also apply to the baum connes conjecture this is discussed in 47 where for example the baum connes conjecture is proved for the full braid groups msc 55n25 homology with local coecients 16s34 group rings laurent rings 57m25 knots and links

sur la convexite holomorphe des revetements lineaires reductifs d une variete projective algebrique complexe let x be a smooth connected compact projective variety over we study the shafarevich conjecture concerning holomorphic convexity along the lines of kollar s approach when the fundamental group of x admits large finite dimensionnal representations we prove that given n the topological covering space widetilde x n of a projective algebraic compact complex manifold x corresponding to the intersection of the kernels of all linear reductive representations of 1 x to gln is holomorphically convex in the surface case this is a corollary of a theorem due to katzarkov and ramachandran

bergman kernels and local holomorphic morse inequalities let x be a hermitian manifold and let lk be a high power of a hermitian holomorphic line bundle over x local versions of demailly s holomorphic morse inequalities that give bounds on the dimension of the dolbeault cohomology groups associated to lk are presented after integration they give the usual holomorphic morse inequalities the local weak inequalities hold on any hermitian manifold x regardless of compactness and completeness the proofs which are elementary are based on a new approach to pointwise bergman kernel estimates where the kernels are estimated by a model kernel in open image in new window

new low roundoff noise realizations of second order digital filter sections new structures for second order filter sections are proposed that yield lower output roundoff noise than many well known structures and are free of zero input limit cycle oscillations these new low roundoff structures are based on these suggested by bomar 1989 and are obtained by putting the constraint that some of the state space coefficients be sum of two power of two terms numerical results are included to illustrate the performance of the proposed structures for narrow band filters and to compare them with other structures

some mixed hodge structures on l 2 cohomology groups of coverings of kahler manifolds we give methods to compute l 2 cohomology groups of a covering manifold obtained by removing the pullback of a normal crossing divisor to a covering of a compact kahler manifold we prove that in suitable quotient categories these groups admit natural mixed hodge structure whose graded pieces are given by the expected gysin maps

low roundoff noise and normal realizations of fixed point iir digital filters explicit design and performance equations are given in terms of the parameters of the desired transfer function h z for two classes of realizations these realizations offer the digital circuit designer an alternative to the usual designs based on direct forms in addition to low roundoff noise these new realizations offer other desirable properties such as low coefficient sensitivities and freedom from overflow oscillations numerical results are presented which detail the design process and verify the theory

berezin quantization and k homology the e theory defined by connes and higson provides a realization of k homology the generalized homology theory dual to k theory based on the notion of asymptotic homomorphisms with this realization it becomes possible to associate a k homology element to a quantization scheme in this article we associate an asymptotic homomorphism and k homology element to the berezin quantization of a bounded symmetric domain further we identify this element with the element of k homology defined by the dolbeault operator of the domain

on the l 2 overline partial cohomology of certain complete kahler metrics let v be a compact and irreducible complex space of complex dimension v whose regular part is endowed with a complete hermitian metric h let pi m rightarrow v be a resolution of v under suitable assumptions on h we prove that begin aligned h v q 2 overline partial mathrm reg v h cong h v q overline partial m quad q 0 ldots v end aligned then we show that the previous isomorphism applies to the case of saper type kahler metrics as introduced by grant melles and milman and to the case of complete kahler metrics with finite volume and pinched negative sectional curvatures

riesz transforms and spectral multipliers of the hodge laguerre operator abstract on r d endowed with the laguerre probability measure we define a hodge laguerre operator l acting on differential forms here is the laguerre exterior differentiation operator defined as the classical exterior differential except that the partial derivatives x i are replaced by the laguerre derivatives x i x i and is the adjoint of with respect to inner product on forms defined by the euclidean structure and the laguerre measure we prove dimension free bounds on l p 1 p for the riesz transforms l 1 2 and l 1 2 as applications we prove the strong hodge de rahm kodaira decomposition for forms in l p and deduce existence and regularity results for the solutions of the hodge and de rham equations in l p we also prove that for suitable functions m the operator m l is bounded on l p 1 p

harmonic maps and constant mean curvature surfaces in h 2 x r we introduce a it hyperbolic gauss map into the poincar e disk for any surface in bbb h 2 times bbb r with regular vertical projection and prove that if the surface has constant mean curvature h 1 2 this hyperbolic gauss map is harmonic conversely we show that every nowhere conformal harmonic map from an open simply connected riemann surface sigma into the poincar e disk is the hyperbolic gauss map of a two parameter family of such surfaces as an application we obtain that any holomorphic quadratic differential on sigma can be realized as the abresch rosenberg holomorphic differential of some and generically infinitely many complete surfaces with h 1 2 in bbb h 2 times bbb r a similar result applies to minimal surfaces in the heisenberg group rm nil 3 finally we classify all complete minimal vertical graphs in bbb h 2 times bbb r

on the parabolic kernel of the schrodinger operator etude des equations paraboliques du type q x t t u x t 0 sur une variete riemannienne generale introduction estimations de gradients inegalites de harnack majorations et minorations des solutions fondamentales equation de la chaleur et noyau de green operateur de schrodinger

spectral flow and dixmier traces abstract we obtain general theorems which enable the calculation of the dixmier trace in terms of the asymptotics of the zeta function and of the heat operator in a general semi finite von neumann algebra our results have several applications we deduce a formula for the chern character of an odd l 1 summable breuer fredholm module in terms of a hochschild 1 cycle we explain how to derive a wodzicki residue for pseudo differential operators along the orbits of an ergodic r n action on a compact space x finally we give a short proof of an index theorem of lesch for generalised toeplitz operators

on the strong l p hodge decomposition over complete riemannian manifolds we establish the strong lp hodge decomposition theorem and the lp poincare inequalities on differential forms over complete non compact riemannian manifolds as applications we prove some lp estimates and existence theorems for the de rham operator as well as some vanishing theorems for the lp cohomology and the lp torsion over complete non compact riemannian manifolds with suitable geometric conditions

fibred surfaces varieties isogenous to a product and related moduli spaces a fibration of an algebraic surface s over a curve b with fibres of genus at least 2 has constant moduli iff it is birational to the quotient of a product of curves by the action of a finite group g a variety isogenous to a higher product is the quotient of a product of curves of genus at least 2 by the free action of a finite group theorem b gives a characterization of surfaces isogenous to a higher product in terms of the fundamental group and of the euler number theorem c classifies the groups thus occurring and shows that after fixing the group and the euler number one obtains an irreducible moduli space the result of theorem b is extended to higher dimension in theorem g thus generalizing cf also theorem h results of jost yau and mok concerning varieties whose universal cover is a polydisk theorem a shows that fibrations where the fibre genus and the genus of the base b are at least 2 are invariants of the oriented differentiable structure the main theorems d and e characterize surfaces carrying constant moduli fibrations as surfaces having a zariski open set satisfying certain topological conditions e g having the right euler number the right fundamental group and the right fundamental group at infinity 0 introduction the study of fibrations of a smooth algebraic surface s over a smooth algebraic curve b lies at the heart of the classification theory and of the geometry of algebraic surfaces our main results in this paper theo rems d e concern a topological characterization of surfaces admitting a constant moduli fibration these results are intimately related to a series of variations on the same theme also in higher dimension and to a circle of allied techniques which we present in the course of the paper the first new result we have in this direction and which is presented in section 2 after we recall several known results some classical some quite recent is the following theorem on the dif ferentiable invariance of the genus of fibres cf theorem 2 9 for a more precise statement theorem a let f s b be a fibration of the surface s over a curve b of genus b 2 and with fibre f of genus g 1 assume that s is another smooth compact kahler surface which is orientedly diffeomorphic to s then the subspace of h 1 s corresponding to f h 1 b determines a fibration f s b with

cohomologie l 2 des varietes qale we give a topological interpretation of the space of l 2 harmonis forms of some qale manifolds introduced by d joyce we introduce a analytical criterium which make possible the used of mayer vietoris sequence

approximating l2 invariants and the atiyah conjecture let g be a torsion free discrete group and let denote the field of algebraic numbers in we prove that g fulfills the atiyah conjecture if g lies in a certain class of groups d which contains in particular all groups that are residually torsion free elementary amenable or are residually free this result implies that there are no nontrivial zero divisors in g the statement relies on new approximation results for l2 betti numbers over g which are the core of the work done in this paper another set of results in the paper is concerned with certain number theoretic properties of eigenvalues for the combinatorial laplacian on l2 cochains on any normal covering space of a finite cw complex we establish the absence of eigenvalues that are transcendental numbers whenever the covering transformation group is either amenable or in the linnell class we also establish the absence of eigenvalues that are liouville transcendental numbers whenever the covering transformation group is either residually finite or more generally in a certain large bootstrap class 2003 wiley periodicals inc

existence and partial regularity results for the heat flow for harmonic maps on considere le probleme d evolution t u m u n u 0 dans m r u 0 u 0 sur m ou m et n sont des varietes de riemann lisses compactes et u 0 l application harmonique de m dans n on demontre l existence d une solution globale faible

erratum to an optimal gap theorem here we shall use the same notations of the original paper the references to equations lemmas propositions theorems are with respect to the paper unless stated otherwise the argument provided for the proof of proposition 3 1 is not complete it overlooks the fact that the solution 2 form x t of the problem 3 1 may contain non trivial 2 0 and 0 2 parts hence proposition 3 1 needs a correction we thank gilles carron for pointing out this oversight in the original proof of proposition 3 1 and his comments we also thank luen fai tam for helpful related discussions we refer interested reader to 5 for an alternate proof of theorem 1 2 since the preservation of the positivity for solution 2 forms solving the problem 3 1 in the paper without knowing that the 2 form being 1 1 type seems elusive even for the 1 1 part projection of the 2 form solutions we replace 3 1 with the following initial boundary value problem on 1 1 form let be a smooth bounded domain in m for a given point p let be the unit outward normal in a small neighborhood near p we

growth of maps distortion in groups and symplectic geometry in the present paper we study two sequences of real numbers associated to a symplectic diffeomorphism the uniform norm of the differential of its n th iteration the word length of its n th iteration where we assume that our diffeomorphism lies in a finitely generated group of symplectic diffeomorphisms we find lower bounds for the growth rates of these sequences in a number of situations these bounds depend on the symplectic geometry of the manifold rather than on the specific choice of a diffeomorphism they are obtained by using recent results of schwarz on floer homology as an application we prove non existence of certain non linear symplectic representations for finitely generated groups

symmetric differentials and the fundamental group helene esnault asked whether a smooth complex projective variety x with infinite fundamental group must have a nonzero symmetric differential meaning that h x s x 6 0 for some i 0 this was prompted by the second author s work 23 in fact severi had wondered in 1949 about possible relations between symmetric differentials and the fundamental group 34 p 36 we know from hodge theory that the cotangent bundle x has a nonzero section if and only if the abelianization of 1x is infinite the geometric meaning of other symmetric differentials is more mysterious and it is intriguing that they may have such a direct relation to the fundamental group in this paper we prove the following result on esnault s question in the slightly broader setting of compact kahler manifolds

kahler parabolicity and the euler number of compact manifolds of non positive sectional curvature let m 2n be a compact riemannian manifold of non positive sectional curvature it is shown that if m 2n is homeomorphic to a kahler manifold then its euler number satisfies the inequality 1 n chi m 2n geq 0

floer homology for magnetic fields with at most linear growth on the universal cover abstract the floer homology of a cotangent bundle is isomorphic to loop space homology of the underlying manifold as proved by abbondandolo and schwarz salamon and weber and viterbo in this paper we show that in the presence of a dirac magnetic monopole which admits a primitive with at most linear growth on the universal cover the floer homology in atoroidal free homotopy classes is again isomorphic to loop space homology as a consequence we prove that for any atoroidal free homotopy class and any sufficiently small 0 any magnetic flow associated to the dirac magnetic monopole has a closed orbit of period belonging to the given free homotopy class in the case where the dirac magnetic monopole admits a bounded primitive on the universal cover we also prove the conley conjecture for hamiltonians that are quadratic at infinity i e we show that such hamiltonians have infinitely many periodic orbits

new second order state space structures for realizing low roundoff noise digital filters several new second order state space digital filter structures are introduced each of the new structures requires one or two less multiplies than the minimum noise structure while achieving a round off noise performance which is nearly as good thus they provide an excellent means of realizing second order subfilters when such subfilters are used to construct nth order filters the reduction in multiplies as compared to using minimum noise subfilters is from about 4n to about 3n an approach to developing simple algebraic real arithmetic design equations for l 2 norm scaled second order structures is presented and then applied to obtaining design equations for the new structures and for the minimum noise structure

geometry of domains with the uniform squeezing property abstract we introduce the notion of domains with uniform squeezing property study various analytic and geometric properties of such domains and show that they cover many interesting examples including teichmuller spaces and hermitian symmetric spaces of non compact type the properties supported by such manifolds include pseudoconvexity hyperconvexity kahler hyperbolicity vanishing of cohomology groups and quasi isometry of various invariant metrics it also leads to nice geometric properties for manifolds covered by bounded domains and a simple criterion to provide positive examples to a problem of serre about stein properties of holomorphic fiber bundles

harmonic maps of bounded symmetric domains harmonic maps between complete and non compact manifolds have been studied by schoen yau li tam aviles choi micallef ding wang and others s y l t a c m and d w for further study it might be of interest to consider problems in various concrete manifolds which are more general than hyperbolic space bounded symmetric domains were introduced by e cartan c1 c2 and were systematically studied by hua look and siegel hi h2 l si those are specific cartan hadamard manifolds whose further geometrical and analytical properties should be explored such investigation might also imply more general results for complete and non compact manifolds the purpose of the present paper is to pursue this goal by the work done by y c wong w a bounded symmetric domain can be viewed as a pseudo grassmannian manifold of all the spacelike subspaces of dimension m in pseudo euclidean space r n of index n in sect 2 this interesting point of view is briefly introduced it is well known that the simplest bounded symmetric domain nm 2 can be identified with a product of two hyperbolic planes he in sect 3 we study harmonic maps into nn 2 via harmonic maps into hyperbolic space and obtain an interesting image shrinking property in the striking paper h o s the authors classified all complete constant mean curvature surfaces in r 3 and 4 with certain restricted gauss image one of the analogous properties in ambient minkowski space was already proved by a different approach in the author s previous paper xi also see a by ruh vilms theorem r v we can investigate submanifolds with parallel mean curvature in euclidean space via its harmonic gauss maps in the present

syzygetic ideals regular sequences and a question of simis let a be a noetherian ring and i an ideal of a simis 7 posed the following question if torf z a z is an a z free module what consequences are brought on i in the present article we consider this question in local noetherian rings our purpose is to give some reasonable additional conditions which ensure that z is generated by a regular sequence the paper is divided into two parts the first one is devoted to obtaining the following result

a sufficient condition for compactness of the neumann operator we show that the existence of a certain family of plurisubharmonic functions on a bounded domain in cn implies that the neumann operator associated to the domain is compact our condition generalizes previous work of catlin on compactness of the neumann operator

characteristic classes and distortion of diffeomorphisms let m and n be manifolds of bounded geometry that is the absolute value of their curvatures as well as their covariant derivatives are bounded from above and their injectivity radii are bounded from below a map f m n has bounded d stortion if there is an upper bound on the norm of the derivative d f a bounded distortion diffeomorphism cb d d is assumed to have an inverse which also has bounded distortion similarly homotopies are assumed to have bounded distortion note that this implies that homotopic maps are a finite distance apart we prove the following theorem that describes when characteristic classes of a compact manifold obstruct the existence of bounded distortion diffeomorphisms of universal covers theorem there are compact manifolds a and b with fundamental group r and a map f a b with jcpcb i pca for some rational pontrjagin class p whose universal cover is b d homotopic to a b d diffeomorphism if and only if r is nonamenable

embeddability of some strongly pseudoconvex cr manifolds we obtain an embedding theorem for compact strongly pseudoconvex cr manifolds which are boundaries of some complete hermitian manifolds we use this to compactify some negatively curved kahler manifolds with compact strongly pseudoconvex boundary an embedding theorem for sasakian manifolds is also derived

topological complexity of symplectic manifolds open access via springer compact agreement the authors wish to thank ay se borat michael farber jarek kedra and john oprea for helpful comments regarding an earlier draft of this paper

a vanishing theorem on generalized cartan hartogs domain of the second type abstract in this paper we consider the vanishing theorem of square integrable harmonic forms with respect to the bergman metric on the second type of generalized cartan hartogs domain by using three main tools the properties of bergman kernel function holomorphic invariant and holomorphic automorphism group

a sobolev mapping property of the bergman kernel we prove that if d is a pseudoconvex domain with lipschitz boundary having an exhaustion function rho such that rho eta is plurisubharmonic then the bergman projection maps the sobolev space w s boundedly to itself for any s eta 2

compact kahler manifolds homotopic to negatively curved riemannian manifolds in this paper we show that any compact kahler manifold homotopic to a compact riemannian manifold with negative sectional curvature admits a kahler einstein metric of general type moreover we prove that on a compact symplectic manifold x homotopic to a compact riemannian manifold with negative sectional curvature for any almost complex structure j compatible with the symplectic form there is no non constant j holomorphic entire curve f mathbb c rightarrow x

quantization of multiply connected manifolds the standard berezin toeplitz geometric quantization of a compact kahler manifold is restricted by integrality conditions these restrictions can be circumvented by passing to the universal covering space provided that the lift of the symplectic form is exact i relate this construction to the baum connes assembly map and prove that it gives a strict quantization of the original manifold i also propose a further generalization classify the required structure and provide a means of computing the resulting algebras these constructions involve twisted group c algebras of the fundamental group which are determined by a group cocycle constructed from the cohomology class of the symplectic form this provides an algebraic counterpart to the morita equivalence of a symplectic manifold with its fundamental group

probability convexity and harmonic maps with small image i uniqueness and fine existence this paper uses probability theory to provide an approach to the dirichlet problem for harmonic maps the probabilistic tools used are those of manifold valued brownian motion and martingales probabilistic proofs are given of uniqueness continuous dependence on data and existence of generalized solutions finely harmonic maps for target domains which have convex geometry this class of domain includes all regular geodesic balls links are made with new results in other fields the martingale dirichlet problem riemannian centres of mass

torus fibrations and localization of index ii local index for acyclic compatible system we give a framework of localization for the index of a dirac type operator on an open manifold suppose the open manifold has a compact subset whose complement is covered by a family of finitely many open subsets each of which has a structure of the total space of a torus bundle under an acyclic condition we define the index of the dirac type operator by using the witten type deformation and show that the index has several properties such as excision property and a product formula in particular we show that the index is localized on the compact set

boundary behavior of harmonic maps on non smooth domains and complete negatively curved manifolds abstract in this paper we develop a theory for harmonic maps which is analogous to the classical theory for bounded harmonic functions in harmonic analysis we solve the dirichlet problem in bounded lipschitz domains and manifolds with negative sectional curvatures generalize the wienner criterion and prove the fatou theorem for harmonic maps into convex balls

a note on euler number of locally conformally kahler manifolds let m 2n be a compact riemannian manifold of non positive resp negative sectional curvature we call m j theta a d bounded locally conformally kahler manifold if the lifted lee form tilde theta on the universal covering space of m is d bounded we show that if m 2n is homeomorphic to a d bounded lck manifold then its euler number satisfies the inequality 1 n chi m 2n ge resp 0

quantum hall effect on the hyperbolic plane in this paper we study both the continuous model and the discrete model of the quantum hall effect qhe on the hyperbolic plane the hall conductivity is identified as a geometric invariant associated to an imprimitivity algebra of observables we define a twisted analogue of the kasparov map which enables us to use the pairing between k theory and cyclic cohomology theory to identify this geometric invariant with a topological index thereby proving the integrality of the hall conductivity in this case

on euler characteristic and fundamental groups of compact manifolds let m be a compact riemannian manifold pi widetilde m rightarrow m be the universal covering and omega be a smooth 2 form on m with pi omega cohomologous to zero suppose the fundamental group pi 1 m satisfies certain radial quadratic resp linear isoperimetric inequality we show that there exists a smooth 1 form eta on widetilde m of linear resp bounded growth such that pi omega d eta as applications we prove that on a compact kahler manifold m omega with pi omega cohomologous to zero if pi 1 m is mathrm cat 0 or automatic resp hyperbolic then m is kahler non elliptic resp kahler hyperbolic and the euler characteristic 1 frac dim mathbb r m 2 chi m ge 0 resp 0

heat equation and compactifications of complete riemannian manifolds soit m une variete de riemann complete dont la courbure de ricci est bornee inferieurement soit m une compactification de m soit f c m on cherche des fonctions f x t c m 0 satisfaisant t f x t 0 x t m 0 f x 0 f x x m f x t f x x t m 0

l 2 cohomology of hyperkahler quotients using an argument of jost and zuo we give a criterion which implies that the l 2 harmonic forms on a complete noncompact hyperkahler manifold lie in the middle dimension and are invariant under the isometry group this is applied to various examples and in particular gives a verification of some of the predictions of sen on monopole moduli spaces

symmetric differentials kahler groups and ball quotients while margulis superrigidity theorem completely describes the finite dimensional linear representations of lattices of higher rank simple real lie groups almost nothing is known concerning the representation theory of complex hyperbolic lattices the main result of this paper theorem 1 3 is a strong rigidity theorem for a certain class of cocompact arithmetic complex hyperbolic lattices it relies on the following two ingredients theorem 1 6 showing that the representations of the topological fundamental group of a compact kahler manifold x are controlled by the global symmetric differentials on x an arithmetic vanishing theorem for global symmetric differentials on certain compact ball quotients using automorphic forms in particular deep results of clozel on base change theorem 1 11

sharp differential estimates of li yau hamilton type for positive p p forms on kahler manifolds in this paper we study the heat equation of hodge laplacian deformation of p p forms on a kahler manifold after identifying the condition and establishing that the positivity of a p p form solution is preserved under such an invariant condition we prove the sharp differential harnack in the sense of liyau hamilton estimates for the positive solutions of the hodge laplacian heat equation we also prove a nonlinear version coupled with the kahler ricci flow and some interpolating matrix differential harnack type estimates for both the kahler ricci flow and the ricci flow 2011 wiley periodicals inc

on the evolution of harmonic maps in higher dimensions on etablit des resultats de regularite partielle et l existence de solutions regulieres globales pour le probleme d evolution pour des applications harmoniques avec des donnees petites

the first l2 betti number of certain homogeneous spaces including classifying spaces for variations of hodge structures in this paper we prove the vanishing of the first l betti number for certain complex homogeneous spaces d g v where g is a semi simple lie group and v is a compact subgroup l cohomology is the appropriate extension of hodge theory for harmonic forms to the case of a noncompact complete manifold x inasmuch as here every l cohomology class can be represented by an l harmonic form see 1 in particular non existence of non trivial l harmonic p forms means that the p th l betti number vanishes besides offering the possibility to extend hodge theory to the noncompact case it can be used to obtain topological information about compact quotients of x by the lindex theorem of atiyah 1 based on this theorem dodziuk singer 4 12 suggested to use l cohomology to approach the hopf conjecture concerning the euler characteristic of riemannian manifolds of non positive curvature which has been verified in several special but important cases 2 3

holder estimates and regularity for holomorphic and harmonic functions in this paper we proved that if a singular manifold satisfies a weak mean value property for positive subharmonic functions then one can derive an oscillation bound for bounded holomorphic functions moreover if we further assume that the volume decays at most polynomially at a singular point

uniqueness of l 1 solutions for the laplace equation and the heat equation on riemannian manifolds on deduit une hypothese geometrique optimale sur une variete de riemann complete qui assure des proprietes d unicite pour des solutions l 1 de l equation de laplace et de la chaleur

uniqueness and regularity of proper harmonic maps introduction the purpose of this paper is to study some uniqueness and regularity properties of the dirichlet problem at infinity for proper harmonic maps between hyperbolic spaces in general if the metrics of two complete noncompact manifolds mm and n are given locally by ds2 imj gij dxzdxj and dsy en h 3 du du respectively then the energy density function of a c1 map u m n is defined by

on pseudo harmonic maps in conformal geometry we extend harmonic map techniques to the setting of more general differential equations in conformal geometry we discuss existence theorems and obtain an extension of siu s strong rigidity to kahler weyl geometry other applications include topological obstructions to the existence of kahler weyl structures for example we show that no co compact lattice in so 1 n n 2 can be the fundamental group of a compact kahler weyl manifold