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作者：Bott, R; Tolman, S; Weitsman, J
作者单位：Harvard University; University of Illinois System; University of Illinois Urbana-Champaign; University of California System; University of California Santa Cruz
摘要：Let G be a compact Lie group, and let LG denote the corresponding loop group. Let (X,omega) be a weakly symplectic Banach manifold. Consider a Hamiltonian action of LG on (X,omega), and assume that the moment map mu:X-->Lg(*) is proper. We consider the function |mu|(2):X-->R, and use a version of Morse theory to show that the inclusion map j:mu(-1)(0)-->X induces a surjection j(*):H-G(*)(X)-->H-G(*)(mu(-1)(0)), in analogy with Kirwan's surjectivity theorem in the finite-dimensional case. We al...
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作者：Nivoche, S
作者单位：Centre National de la Recherche Scientifique (CNRS); Universite de Toulouse; Universite Toulouse III - Paul Sabatier
摘要：We prove a conjecture of Zahariuta which itself solves a problem of Kolmogorov on the epsilon-entropy of some classes of analytic functions. For a given holomorphically convex compact subset K in a pseudoconvex domain D in C-n, Zahariuta's conjecture consists in approximating the relative extremal function u* (K,D), uniformly on any compact subset of D \ K, by pluricomplex Green functions on D with logarithmic poles in the compact subset K.
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作者：Liu, Q; Lorenzini, D; Raynaud, M
作者单位：Universite de Bordeaux; Centre National de la Recherche Scientifique (CNRS); University System of Georgia; University of Georgia; Universite Paris Saclay
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作者：Ozawa, N; Popa, S
作者单位：University of Tokyo; University of California System; University of California Los Angeles
摘要：We prove several unique prime factorization results for tensor products of type II1 factors coming from groups that can be realized either as subgroups of hyperbolic groups or as discrete subgroups of connected Lie groups of real rank 1. In particular, we show that if Rcircle timesLF(r 1) circle times...circle times LFr m is isomorphic to a subfactor in Rcircle timesLF(s 1) circle times...circle times LFs n, for some 2less than or equal tor(i), s(j)less than or equal toinfinity, then mless tha...
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作者：Rodnianski, I; Schlag, W
作者单位：Princeton University; California Institute of Technology
摘要：In this paper we establish dispersive estimates for solutions to the linear Schrodinger equation in three dimensions (0.1) 1/ipartial derivative(t)psi - Deltapsi + Vpsi = 0 psi(s) = f where V(t,x) is a time-dependent potential that satisfies the conditions [GRAPHICS] Here c(0) is some small constant and V((tau) over cap, x) denotes the Fourier transform with respect to the first variable. We show that under these conditions (0.1) admits solutions psi(.) is an element of L-t(infinity)(L-x(2)(R-...
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作者：Suter, R
作者单位：Swiss Federal Institutes of Technology Domain; ETH Zurich
摘要：Let g be a complex simple Lie algebra and b a fixed Borel subalgebra of g. We describe the abelian ideals in b in a uniform way, that is, independent of the classification of complex simple Lie algebras. As an application we derive a formula for the maximal dimension of a commutative Lie subalgebra of g.
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作者：Götze, F
作者单位：University of Bielefeld
摘要：For d-dimensional ellipsoids E with dgreater than or equal to5 we show that the number of lattice points in rE is approximated by the volume of rE, as r tends to infinity, up to an error of order O(r(d-2)) for general ellipsoids and up to an error of order o(r(d-2)) for irrational ones. The estimate refines earlier bounds of the same order for dimensions dgreater than or equal to9. As an application a conjecture of Davenport and Lewis about the shrinking of gaps between large consecutive value...
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作者：Haskins, M
作者单位：Johns Hopkins University
摘要：We prove a number of results on the geometric complexity of special Lagrangian (SLG) T-2-cones in C-3. Every SLG T-2-cone has a fundamental integer invariant, its spectral curve genus. We prove that the spectral curve genus of an SLG T-2-cone gives a lower bound for its geometric complexity, i.e. the area, the stability index and the Legendrian index of any SLG T-2-cone are all bounded below by explicit linearly growing functions of the spectral curve genus. We prove that the cone on the Cliff...
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作者：Golse, F; Saint-Raymond, L
作者单位：Institut Universitaire de France; Universite PSL; Ecole Normale Superieure (ENS); Sorbonne Universite
摘要：The present work establishes a Navier-Stokes limit for the Boltzmann equation considered over the infinite spatial domain R-3. Appropriately scaled families of DiPerna-Lions renormalized solutions are shown to have fluctuations whose limit points (in the w-L-1 topology) are governed by Leray solutions of the limiting Navier-Stokes equations. This completes the arguments in Bardos-Golse-Levermore [Commun. Pure Appl. Math. 46(5), 667-753 (1993)] for the steady case, and in Lions-Masmoudi [Arch. ...
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作者：Pasquale, A
作者单位：TU Clausthal
摘要：We define the Theta-hypergeometric functions as a generalization of the hypergeometric functions associated with root systems of Heckman and Opdam. In the geometric setting, the Theta-hypergeometric functions can be specialized to Harish-Chandra's spherical functions on Riemannian symmetric spaces of noncompact type, and also to the spherical functions on noncompactly causal symmetric spaces. After describing their regularity properties, we prove estimates for the Theta-hypergeometric function...
