gromov witten classes quantum cohomology and enumerative geometry the paper is devoted to the mathematical aspects of topological quantum field theory and its applications to enumerative problems of algebraic geometry in particular it contains an axiomatic treatment of gromov witten classes and a discussion of their properties for fano varieties cohomological field theories are defined and it is proved that tree level theories are determined by their correlation functions application to counting rational curves on del pezzo surfaces and projective spaces are given

on the cohomology of stable map spaces we describe an approach to calculating the cohomology rings of stable map spaces m0 0 n d

orbifold quasimap theory we extend to orbifolds the quasimap theory of ciocan fontanine and kim adv math 225 6 3022 3051 2010 j geom phys 75 17 47 2014 as well as the genus zero wall crossing results from algebr geom 1 4 400 448 2014 proceedings of the conference on the occasion of mukai s 60th birthday 2015 as a consequence we obtain generalizations of orbifold mirror theorems in particular of the mirror theorem for toric orbifolds recently proved independently by coates et al a mirror theorem for toric stacks

git compactifications of m0 n and flips abstract we use geometric invariant theory git to construct a large class of compactifications of the moduli space m 0 n these compactifications include many previously known examples as well as many new ones as a consequence of our git approach we exhibit explicit flips and divisorial contractions between these spaces

on lattices with a smallest set of aggregation functions given a bounded lattice l with bounds 0 and 1 it is well known that the set pol 0 1 l of all 0 1 preserving polynomials of l forms a natural subclass of the set c l of aggregation functions on l the main aim of this paper is to characterize all finite lattices l for which these two classes coincide i e when the set c l is as small as possible these lattices are shown to be completely determined by their tolerances also several sufficient purely lattice theoretical conditions are presented in particular all simple relatively complemented lattices or simple lattices for which the join meet of atoms coatoms is 1 0 are of this kind

on the lp norm of spectral clusters for compact manifolds with boundary we use microlocal and paradifferential techniques to obtain l8 norm bounds for spectral clusters associated with elliptic second order operators on two dimensional manifolds with boundary the result leads to optimal lq bounds in the range 2 q for l2 normalized spectral clusters on bounded domains in the plane and more generally for two dimensional compact manifolds with boundary we also establish new sharp lq estimates in higher dimensions for a range of exponents qn q

moduli spaces of hyperelliptic curves with a and d singularities we introduce moduli spaces of quasi admissible hyperelliptic covers with at worst a and d singularities the stability conditions for these moduli spaces depend on two rational parameters describing allowable singularities for the extreme values of the parameters we obtain the stacks of stable limits of a n and d n singularities and the quotients of the miniversal deformation spaces of these singularities by natural mathbb g m actions we interpret the intermediate spaces as log canonical models of the stacks of stable limits of a n and d n singularities

the ring of evenly weighted points on the line let m w mathbb p 1 n hbox sl 2 denote the geometric invariant theory quotient of mathbb p 1 n by the diagonal action of hbox sl 2 using the line bundle mathcal o w 1 w 2 ldots w n on mathbb p 1 n let r w be the coordinate ring of m w we give a closed formula for the hilbert function of r w which allows us to compute the degree of m w the graded parts of r w are certain kostka numbers so this hilbert function computes stretched kostka numbers if all the weights w i are even we find a presentation of r w so that the ideal i w of this presentation has a quadratic grobner basis in particular r w is koszul we obtain this result by studying the homogeneous coordinate ring of a projective toric variety arising as a degeneration of m w

aggregation on boolean multi polar space three types of aggregation operators defined on a boolean multi polar space 0 1 m are compared three different monotonicity conditions that yield different types of aggregation operators are discussed and the structure of these aggregation operators on 0 1 m with additional properties of associativity and commutativity is studied for any m n the commutative associative boolean multi polar aggregation operators are shown to coincide with boolean multi polar uninorms the structure of commutative associative sl aggregation operators is shown to be dependent on the structure of the class of abelian idempotent semigroups based on m 1 elements with an annihilator we show that each commutative associative sl aggregation operator with annihilator 0 corresponds to a lower semi lattice with bottom element 0 for m 2 the class of commutative associative c aggregation operators is proved to be equal to the intersection of the class of commutative associative boolean multi polar aggregation operators and the class of commutative associative sl aggregation operators examples of the three types of commutative associative aggregation operators are shown and discussed for m 1 2 3

towards a classification of modular compactifications of mathcal m _ g n the moduli space of smooth curves admits a beautiful compactification mathcal m g n subset overline mathcal m g n by the moduli space of stable curves in this paper we undertake a systematic classification of alternate modular compactifications of mathcal m g n let mathcal u g n be the non separated moduli stack of all n pointed reduced connected complete one dimensional schemes of arithmetic genus g when g 0 mathcal u 0 n is irreducible and we classify all open proper substacks of mathcal u 0 n when g 1 mathcal u g n may not be irreducible but there is a unique irreducible component mathcal v g n subset mathcal u g n containing mathcal m g n we classify open proper substacks of mathcal v g n satisfying a certain stability condition

multi and multi polar capacities aggregation of inputs from different categories generalizes both unipolar standard and bipolar aggregation this aggregation covers two main cases of multi polar and non monotone aggregation inputs from different categories can be found in classification methods multi criteria decision making game theory and political and sociological sciences two main concepts related to aggregation on the unit interval are capacities and aggregation on grid points boolean functions in this paper multi and multi polar capacities that extend bi and bipolar capacities are introduced the position of these capacities is clarified by means of the connection between boolean crisp functions capacities aggregation and concepts from other domains of science which are shown for the unipolar the bipolar and the multi polar case the connection between multi and multi polar capacities and the concept of games with n players and r alternatives is described

log canonical models of elliptic surfaces abstract we classify the log canonical models of elliptic surface pairs f x c s f a where f x c is an elliptic fibration s is a section and f a is a weighted sum of marked fibers in particular we show how the log canonical models depend on the choice of the weights we describe a wall and chamber decomposition of the space of weights based on how the log canonical model changes in addition we give a generalized formula for the canonical bundle of an elliptic surface with section and marked fibers this is the first step in constructing compactifications of moduli spaces of elliptic surfaces using the minimal model program

descendant invariants and characteristic numbers on a stack of stable maps the cotangent line classes are modified by subtracting certain boundary divisors these modified cotangent line classes are compatible with forgetful morphisms and are well suited to enumerative geometry tangency conditions allow simple expressions in terms of modified cotangent line classes topological recursion relations are established among their top products in genus 0 yielding effective recursions for characteristic numbers of rational curves in any projective homogeneous variety in higher genus the obtained numbers are only virtual due to contributions from spurious components of the space of maps for the projective plane the necessary corrections are determined in genus 1 and 2 to give the characteristic numbers in these cases

weighted projective embeddings stability of orbifolds and constant scalar curvature kahler metrics we embed polarised orbifolds with cyclic stabiliser groups into weighted projective space via a weighted form of kodaira embedding dividing by the non reductive automorphisms of weighted projective space then formally gives a moduli space of orbifolds we show how to express this as a reductive quotient and so a git problem thus defining a notion of stability for orbifolds we then prove an orbifold version of donaldson s theorem the existence of an orbifold kahler metric of constant scalar curvature implies k semistability by extending the notion of slope stability to orbifolds we therefore get an explicit obstruction to the existence of constant scalar curvature orbifold kahler metrics we describe the manifold applications of this orbifold result and show how many previously known results troyanov ghigi kollar rollin singer the adscft sasaki einstein obstructions of gauntlett martelli sparks yau fit into this framework

description of sup and inf preserving aggregation functions via families of clusters in data tables abstract connection between the theory of aggregation functions and formal concept analysis is discussed and studied thus filling a gap in the literature by building a bridge between these two theories one of them living in the world of data fusion the second one in the area of data mining we show how galois connections can be used to describe an important class of aggregation functions preserving suprema and by duality to describe aggregation functions preserving infima our discovered method gives an elegant and complete description of these classes also possible applications of our results within certain biclustering fuzzy fca based methods are discussed

determining anisotropic real analytic conductivities by boundary measurements if an electrical potential is applied to the surface of a solid body the current flux across the surface depends on the conductivity in the interior of the body we want to consider the inverse problem of determining the conductivity by these boundary measurements

towards the ample cone of mg n in this paper we study the ample cone of the moduli space m g n of stable n pointed curves of genus g our motivating conjecture is that a divisor on m g n is ample iff it has positive intersection with all 1 dimensional strata the components of the locus of curves with at least 3g n 2 nodes this translates into a simple conjectural description of the cone by linear inequalities and as all the 1 strata are rational includes the conjecture that the mori cone is polyhedral and generated by rational curves our main result is that the conjecture holds iff it holds for g 0 more precisely there is a natural finite map r m0 2g n m g n whose image is the locus rg n of curves with all components rational any 1 strata either lies in rg n or is numerically equivalent to a family e of elliptic tails and we show that a divisor d is nef iff d e 0 and r d is nef we also give results on contractions i e morphisms with connected fibers to projective varieties of m g n for g 1 showing that any fibration factors through a tautological one given by forgetting points and that the exceptional locus of any birational contraction is contained in the boundary

riemannian manifolds with maximal eigenfunction growth on any compact riemannian manifold m g of dimension n the l sp 2 normalized eigenfunctions phi sb lambda satisfy lvert rvert phi sb lambda lvert rvert sb infty leq c lambda sp n 1 2 where delta phi sb lambda lambda sp 2 phi sb lambda the bound is sharp in the class of all m g since it is obtained by zonal spherical harmonics on the standard n sphere s sp n but of course it is not sharp for many riemannian manifolds for example for flat tori mathbb r sp n gamma we say that s sp n but not mathbb r sp n gamma is a riemannian manifold with maximal eigenfunction growth the problem that motivates this paper is to determine the m g with maximal eigenfunction growth our main result is that such an m g must have a point x where the set mathscr l sb x of geodesic loops at x has positive measure in s sp ast sb xm we show that if m g is real analytic this puts topological restrictions on m for example only m s sp 2 or m mathbb r p sp 2 topologically in dimension 2 can possess a real analytic metric of maximal eigenfunction growth we further show that generic metrics on any m fail to have maximal eigenfunction growth in addition we construct an example of m g for which mathscr l sb x has positive measure for an open set of x but which does not have maximal eigenfunction growth thus it disproves a naive converse to the main result

tautological classes on the moduli spaces of stable maps to p r via torus actions we present a localization proof of the fact that the cohomology of the moduli spaces of genus zero stable maps to projective spaces is entirely tautological in addition we obtain a description of a bialynicki birula decomposition of the stack of stable maps in the context of gathmann s moduli spaces of maps with prescribed contact order to a fixed hyperplane we show that the decomposition is filterable

the analysis of partial differential operators i hormander springer 1985 vol 1 391 pp vol 2 390 pp vol 3 525 pp vol 4 351 pp

intermediate moduli spaces of stable maps we describe the chow ring with rational coefficients of overline m 0 1 mathbb p n d as the subring of invariants of a ring b overline m 0 1 mathbb p n d mathbb q relative to the action of the group of symmetries sd we compute b overline m 0 1 mathbb p n d mathbb q by following a sequence of intermediate spaces for overline m 0 1 mathbb p n d

towards mori s program for the moduli space of stable maps we introduce and compute the class of a number of effective divisors on the moduli space of stable maps overline scr m 0 0 bbb p r d which for small d provide a good understanding of the extremal rays and the stable base locus decomposition for the effective cone we also discuss various birational models that arise in mori s program including the hilbert scheme the chow variety the space of k stable maps the space of branchcurves and the space of semi stable sheaves

concerning the lp norm of spectral clusters for second order elliptic operators on compact manifolds in this paper we study the lp l2 mapping properties of a spectral projection operator for riemannian manifolds this operator is a generalization of the harmonic projection operator for spherical harmonics on s see c d sogge duke math j 53 1986 43 65 among other things we generalize the l2 restriction theorems of c fefferman e m stein and p tomas bull amer math sot 81 1975 477478 for the fourier transform in r to the setting of riemannian manifolds we obtain these results for the spectral projection operator as a corollary of a certain sobolev inequality involving d r2 for large r this sobolev inequality generalizes certain results for r of c kenig a ruiz and the author duke math j 55 1987 329 347 the main tools in the proof of the sobolev inequalities for riemannian manifolds are the hadamard parametrix cf l hbrmander acta mad 88 1968 341 370 and the analysis of linear partial differential equations vol iii springer verlag new york 1985 and oscillatory integral theorems of l carleson and p sjolin studia math 44 19x 287 299 and stein arm math stud 112 1986 307 357 0 1988 academic pnss iw

the geometry of stable quotients in genus one stable quotients provide an alternative to stable maps for compactifying spaces of maps when n ge 2 the space overline q g mathbb p n 1 d overline q g g 1 n d compactifies the space of degree d maps of smooth genus g curves to mathbb p n 1 while overline q g g 1 1 d simeq overline m 1 d cdot epsilon s d is a quotient of a hassett weighted pointed space in this paper we study the coarse moduli schemes associated to the smooth proper deligne mumford stacks overline q 1 mathbb p n 1 d for all n ge 1 we show these schemes are projective unirational and have picard number 2 then we give generators for the picard group compute the canonical divisor the cones of ample divisors and in the case n 1 the cones of effective divisors we conclude that overline q 1 mathbb p n 1 d is fano if and only if n d 1 d 2 20 moreover we show that overline q 1 mathbb p n 1 d is a mori fiber space for all n d hence always minimal in the sense of the minimal model program in the case n 1 we write in addition a closed formula for the poincare polynomial

square tiled surfaces and rigid curves on moduli spaces abstract we study the algebro geometric aspects of teichmuller curves parameterizing square tiled surfaces with two applications a there exist infinitely many rigid curves on the moduli space of hyperelliptic curves they span the same extremal ray of the cone of moving curves their union is a zariski dense subset hence they yield infinitely many rigid curves with the same properties on the moduli space of stable n pointed rational curves for even n b the limit of slopes of teichmuller curves and the sum of lyapunov exponents for the teichmuller geodesic flow determine each other which yields information about the cone of effective divisors on the moduli space of curves

git stability of weighted pointed curves in the late 1970s mumford established chow stability of smooth unpointed genus g curves embedded by complete linear systems of degree d 2g 1 and at about the same time gieseker established asymptotic hilbert stability that is stability of m th hilbert points for some large values of m under the same hypotheses both of them then use an indirect argument to show that nodal deligne mumford stable curves are git stable the case of marked points lay untouched until 2006 when elizabeth baldwin proved that pointed deligne mumford stable curves are asymptotically hilbert stable actually she proved this for stable maps which includes stable curves as a special case her argument is a delicate induction on g and the number of marked points n elliptic tails are glued to the marked points one by one ultimately relating stability of an n pointed genus g curve to gieseker s result for genus g n unpointed curves there are three ways one might wish to improve upon baldwin s results first one might wish to construct moduli spaces of weighted pointed curves or maps it appears that baldwin s proof can accommodate some but not all sets of weights second one might wish to study hilbert stability for small values of m since baldwin s proof uses gieseker s proof as the base case it is not easy to see how it could be modified to yield an approach for small m finally the minimal model program for moduli spaces of curves has generated interest in git for 2 3 or 4 canonical linear systems due to its use of elliptic tails baldwin s proof cannot be used to study these as elliptic tails are known to be git unstable in these cases in this paper i give a direct proof that smooth curves with distinct weighted marked points are asymptotically hilbert stable with respect to a wide range of parameter spaces and linearizations some of these yield the coarse moduli space of deligne mumford stable pointed curves m g n and hassett s moduli spaces of weighted pointed curves m g a while other linearizations may give other quotients which are birational to these and which may admit interpretations as moduli spaces the full construction of the moduli spaces is not contained in this paper only the proof that smooth curves with distinct weighted marked points are stable which is the key new result needed for the construction for this i follow gieseker s approach to reduce to the git problem to a combinatorial problem though the solution is very different

spectral theory for perturbed krein laplacians in nonsmooth domains abstract we study spectral properties for h k the krein von neumann extension of the perturbed laplacian v defined on c 0 where v is measurable bounded and nonnegative in a bounded open set r n belonging to a class of nonsmooth domains which contains all convex domains along with all domains of class c 1 r r 1 2 in particular in the aforementioned context we establish the weyl asymptotic formula j n k j 2 n v n n 2 o n 1 2 2 as where v n n 2 n 2 1 denotes the volume of the unit ball in r n and k j j n are the non zero eigenvalues of h k listed in increasing order according to their multiplicities we prove this formula by showing that the perturbed krein laplacian i e the krein von neumann extension of v defined on c 0 is spectrally equivalent to the buckling of a clamped plate problem and using an abstract result of kozlov from the mid 1980s our work builds on that of grubb in the early 1980s who has considered similar issues for elliptic operators in smooth domains and shows that the question posed by alonso and simon in 1980 pertaining to the validity of the above weyl asymptotic formula continues to have an affirmative answer in this nonsmooth setting we also study certain exterior type domains r n k n 3 with k r n compact and vanishing bessel capacity b 2 2 k 0 to prove equality of friedrichs and krein laplacians in l 2 d n x that is c 0 has a unique nonnegative self adjoint extension in l 2 d n x

a finite element solution of an added mass formulation for coupled fluid solid vibrations a finite element method to approximate the vibration modes of a structure in contact with an incompressible fluid is analyzed in this paper the effect of the fluid is taken into account by means of an added mass formulation which is one of the most usual procedures in engineering practice gravity waves on the free surface of the liquid are also considered in the model piecewise linear continuous elements are used to discretize the solid displacements the variables to compute the added mass terms and the vertical displacement of the free surface yielding a non conforming method for the spectral coupled problem error estimates are settled for approximate eigenfunctions and eigenfrequencies implementation issues are discussed and numerical experiments are reported in particular the method is compared with other numerical scheme based on a pure displacement formulation which has been recently analyzed

multipolar aggregation operators in reasoning methods for fuzzy rule based classification systems the reasoning methods in fuzzy rule based classification systems are studied and their relation to multipolar aggregation operators is discussed we describe the change in the output of the classification system based on the change of the fuzzy reasoning method we propose a new fuzzy reasoning method based on multipolar fusion owa operator which can control the transition between the maximum rule method and the maximum vote method by a weighting vector this new method uses principles of owa operators and assigns the rule weight according to the strength of activation of the rule we compare different fuzzy reasoning methods in case studies

universal relations on stable map spaces in genus zero we introduce a factorization for the map between moduli spaces of stable maps which forgets one marked point this leads to a study of universal relations in the cohomology of stable map spaces in genus zero

higher genus wall crossing in landau ginzburg theory abstract for a fermat quasi homogeneous polynomial we study the associated weighted fan jarvis ruan witten theory with narrow insertions we prove a wall crossing formula in all genera via localization on a master space which is constructed by introducing an additional tangent vector to the moduli problem this is a landau ginzburg theory analogue of the higher genus quasi map wall crossing formula proved by ciocan fontanine and kim it generalizes the genus 0 result by ross ruan and the genus 1 result by guo ross

a reconstruction theorem in quantum cohomology and quantum k theory a reconstruction theorem for genus 0 gravitational quantum cohomology and quantum k theory is proved a new linear equivalence in the picard group of the moduli space of genus 0 stable maps relating the pull backs of line bundles from the target via different markings is used for the reconstruction result examples of calculations in quantum cohomology and quantum k theory are given

decomposable and k additive multi capacities and multi polar capacities extensions of several concepts for definition of capacities given by a small number of parameters in the unipolar and bipolar framework to the case of multi polar input spaces are studied the paper covers decomposable symmetric category symmetric additive reduced additive and k additive multi polar capacities and discusses its properties the multi polar mobius transform of multi polar capacities is introduced and its properties for coordinate wisely given additive and k additive multi polar capacities are described

projectivity of the moduli space of stable log varieties and subadditivity of log kodaira dimension reference epfl article 231100doi 10 1090 jams 871 url http dx doi org 10 1090 jams 871 record created on 2017 09 19 modified on 2017 10 02

a new look at the moduli space of stable hyperelliptic curves we carry out the log minimal model program for the moduli space bar h g of stable hyperelliptic curves and show that certain log canonical models of bar h g are isomorphic to the proper transform of bar h g in the corresponding log canonical models of bar m g for g 3 we retrieve the compact moduli space bar b 8 of binary forms as a log canonical model and obtain a decomposition of the natural map bar h 3 to bar b 8 into successive divisorial contractions of the boundary divisors as a byproduct we also obtain an isomorphism of bar b 8 with the git quotient of the chow variety of bicanonically embedded hyperelliptic curves of genus three

hypertrees projections and moduli of stable rational curves we give a conjectural description for the cone of effective divisors of the grothendieck knudsen moduli space m 0 n of stable ra tional curves with n marked points namely we introduce new combi natorial structures called hypertrees and show that they give exceptional divisors onm 0 n with many remarkable properties x1 introduction a major open problem inspired by the pioneering work of harris and mumford hm on the kodaira dimension of the moduli space of stable curves is to understand geometry of its birational models and in particular to describe its cone of effective divisors and a decomposition of this cone into mori chambers hk encoding ample divisors on birational models here we study the genus zero case the moduli spaces m 0 n parame trize stable rational curves i e nodal trees of p 1 s with n marked points and without automorphisms for any subseti of marked points m 0 n has a natural boundary divisor i whose general element parametrizes stable rational curves with two irreducible components one marked by points in i and another marked by points ini c we will introduce new combinatorial objects called hypertrees with an eye towards the following 1 1 conjecture the effective cone of m 0 n is generated by boundary divisors and by divisorsd defined below parametrized by irreducible hypertrees

intersection theory of moduli space of stable n pointed curves of genus zero we give a new construction of the moduli space via a composition of smooth codimension two blowups and use our construction to determine the chow ring

a virtual fundamental class construction for the moduli space of c n equivariant morphisms abstract let x be a smooth projective variety with the action of c n the article describes the moduli space of c n equivariant morphisms from stable toric varieties into x as the inverse limit of the git quotients of x and their flips when these spaces are enhanced with a naturally associated deligne mumford stack structure this description is used for constructing a class in the chow group of the moduli space of dimension dim x n which is invariant under equivariant deformations of x

moduli spaces of weighted pointed stable curves abstract a weighted pointed curve consists of a nodal curve and a sequence of marked smooth points each assigned a number between zero and one a subset of the marked points may coincide if the sum of the corresponding weights is no greater than one we construct moduli spaces for these objects using methods of the log minimal model program and describe the induced birational morphisms between moduli spaces as the weights are varied in the genus zero case we explain the connection to geometric invariant theory quotients of points in the projective line and to compactifications of moduli spaces studied by kapranov keel and losev manin

multi polar t conorms and uninorms abstract transformation of uninorms defined on the unit interval to the bipolar scale yields bipolar t conorms and transformation of nullnorms on the unit interval yields bipolar t norms we use this relation in the investigation of the structure of bipolar and multi polar t norms and t conorms we use the same transformation of the unit interval into the bipolar scale in order to obtain bipolar aggregation operators from ordinal sum t norms and t conorms the extensions of these special bipolar aggregation operators generalize both multi polar t norms and t conorms and therefore we call them multi polar uninorms several examples of multi polar t conorms and uninorms are also presented

the intrinsic normal cone let x be an algebraic stack in the sense of deligne mumford we construct a purely 0 dimensional algebraic stack over x in the sense of artin the intrinsic normal cone frak c x the notion of perfect obstruction theory for x is introduced and it is shown how to construct given a perfect obstruction theory for x a pure dimensional virtual fundamental class in the chow group of x we then prove some properties of such classes both in the absolute and in the relative context via a deformation theory interpretation of obstruction theories we prove that several kinds of moduli spaces carry a natural obstruction theory and sometimes a perfect one

the first steklov eigenvalue conformal geometry and minimal surfaces we consider the relationship of the geometry of compact riemannian manifolds with boundary to the first nonzero eigenvalue 1 of the dirichlet to neumann map steklov eigenvalue for surfaces with genus and k boundary components we obtain the upper bound 1l 2 k for 0 and k 1 this result was obtained by weinstock in 1954 and is sharp we attempt to find the best constant in this inequality for annular surfaces 0 and k 2 for rotationally symmetric metrics we show that the best constant is achieved by the induced metric on the portion of the catenoid centered at the origin which meets a sphere orthogonally and hence is a solution of the free boundary problem for the area functional in the ball for a general class of not necessarily rotationally symmetric metrics on the annulus which we call supercritical we prove that 1 l is dominated by that of the critical catenoid with equality if and only if the annulus is conformally equivalent to the critical catenoid by a conformal transformation which is an isometry on the boundary motivated by the annulus case we show that a proper submanifold of the ball is immersed by steklov eigenfunctions if and only if it is a free boundary solution we then prove general upper bounds for conformal metrics on manifolds of any dimension which can be properly conformally immersed into the unit ball in terms of certain conformal volume quantities we show that these bounds are only achieved when the manifold is minimally immersed by first steklov eigenfunctions we also use these ideas to show that any free boundary solution in two dimensions has area at least and we observe that this implies the sharp isoperimetric inequality for free boundary solutions in the two dimensional case

chow groups of the moduli spaces of weighted pointed stable curves of genus zero abstract the moduli space m a of weighted pointed stable curves of genus zero is stratified according to the degeneration types of such curves we show that the homology groups of m a are generated by the strata of m a and give all additive relations between them we also observe that the chow groups a i m a and the homology groups h 2 i m a are isomorphic this generalizes kontsevich manin s and losev manin s theorems to arbitrary weight data a

on the biregular geometry of the fulton macpherson compactification abstract let x n be the fulton macpherson compactification of the configuration space of n ordered points on a smooth projective variety x we prove that if either n 2 or dim x 2 then the connected component of the identity of aut x n is isomorphic to the connected component of the identity of aut x when x c is a curve of genus g c 1 we classify the dominant morphisms c n c r and thanks to this we manage to compute the whole automorphism group of c n namely aut c n s n aut c for any n 2 while aut c 2 s 2 aut c aut c furthermore we extend these results on the automorphisms to the case where x c 1 c r is a product of curves of genus g c i 2 finally using the techniques developed to deal with fulton macpherson spaces we study the automorphism groups of some kontsevich moduli spaces m 0 n p n d

the weyl type asymptotic formula for biharmonic steklov eigenvalues on riemannian manifolds abstract let be a bounded domain with c 2 smooth boundary in an n dimensional oriented riemannian manifold it is well known that for the biharmonic equation 2 u 0 in with the condition u 0 on there exists an infinite set u k of biharmonic functions in with positive eigenvalues k satisfying u k k u k 0 on in this paper by a new method we establish the weyl type asymptotic formula for the counting function of the biharmonic steklov eigenvalues k

averaging operators in fuzzy classification systems the averaging operators used for aggregation of outputs of fuzzy classification rules are examined several methods used in fuzzy rule based classification systems are discussed and related multi polar averaging operators are shown further new aggregation methods based on the idea used for the definition of owa operators are described the connection between multi polar averaging operators and the multi polar choquet integral is shown and using this connection the conditions under which are the respective averaging operators monotone are studied several examples of special multi polar owa operators with a relation to existing bipolar aggregation operators are included

tautological rings of stable map spaces we find a set of generators and relations for the system of extended tautological rings associated to the moduli spaces of stable maps in genus zero admitting a simple geometrical interpretation in particular when the target is p n these give a complete presentation for the cohomology and chow rings in the cases with without marked points

variation of cone metrics on riemann surfaces we discuss the variational properties of the unique conical metric of constant curvature 1 associated to a compact riemann surface together with a weighted divisor 2005 elsevier inc all rights reserved

on asymptotic properties of biharmonic steklov eigenvalues abstract in this paper by explicitly calculating the principal symbols of pseudodifferential operators we establish two weyl type asymptotic formulas with sharp remainder estimates for the counting functions of the two classes of biharmonic steklov eigenvalue problems of smooth bounded domains in a riemannian manifold

signed and sign changing solutions of bi nonlocal fourth order elliptic problem we study a class of nonlocal fourth order elliptic problem which is seldom studied because of the presence of the biharmonic operator and binonlocal terms we are interested in the existence of signed and sign changing solutions our approach is based on variational invariant sets of descending flow and cone theory our results extend and improve some recent work we study a class of nonlocal fourth order elliptic problem which is seldom studied because of the presence of the biharmonic operator and binonlocal terms we are interested in the existence of signed and sign changing solutions our approach is based on variational invariant sets of descending flow and cone theory our results extend and improve some recent work

sharp bounds for the first non zero stekloff eigenvalues abstract let m be an n 2 dimensional compact riemannian manifold with boundary and non negative ricci curvature consider the following two stekloff eigenvalue problems u 0 in m u p u on m 2 u 0 in m u u q u 0 on m where is the laplacian operator on m and denotes the outward unit normal on m the first non zero eigenvalues of the above problems will be denoted by p 1 and q 1 respectively in the present paper we prove that if the principle curvatures of the second fundamental form of m are bounded below by a positive constant c then p 1 1 1 1 n 1 c 2 n 1 c with equality holding if and only if is isometric to an n dimensional euclidean ball of radius 1 c here 1 denotes the first non zero eigenvalue of the laplacian of m we also show that if the mean curvature of m is bounded below by a positive constant c then q 1 n c with equality holding if and only if m is isometric to an n dimensional euclidean ball of radius 1 c finally we show that q 1 a v and that if the equality holds and if there is a point x 0 m such that the mean curvature of m at x 0 is no less than a n v then m is isometric to an n dimensional euclidean ball being a and v the area of m and the volume of m respectively

the κ ring of the moduli of curves of compact type the subalgebra of the tautological ring of the moduli of curves of compact type generated by the classes is studied in all genera relations constructed via the virtual geometry of the moduli of stable quotients are used to obtain minimal sets of generators bases and betti numbers of the rings are computed a universality property relating the higher genus rings to the genus 0 rings is proven using the virtual geometry of the moduli space of stable maps the g formula for hodge integrals arises as the simplest consequence