2期

最新文章

• Length spectra and degeneration of flat metrics AI翻译
  作者：Duchin, Moon; Leininger, Christopher J.; Rafi, Kasra
  作者单位：University of Michigan System; University of Michigan; University of Illinois System; University of Illinois Urbana-Champaign; University of Oklahoma System; University of Oklahoma - Norman
  摘要：In this paper we consider flat metrics (semi-translation structures) on surfaces of finite type. There are two main results. The first is a complete description of when a set of simple closed curves is spectrally rigid, that is, when the length vector determines a metric among the class of flat metrics. Secondly, we give an embedding into the space of geodesic currents and use this to obtain a compactification for the space of flat metrics. The geometric interpretation is that flat metrics deg...
• Metric differentiation, monotonicity and maps to L1 AI翻译
  作者：Cheeger, Jeff; Kleiner, Bruce
  作者单位：New York University
  摘要：This is one of a series of papers on Lipschitz maps from metric spaces to L-1. Here we present the details of results which were announced in Cheeger and Kleiner (Ann. Math., 2006, to appear, arXiv:math.MG/0611954, Sect. 1.8): a new approach to the infinitesimal structure of Lipschitz maps into L-1, and, as a first application, an alternative proof of the main theorem of Cheeger and Kleiner (Ann. Math., 2006, to appear, arXiv: math. MG/0611954), that the Heisenberg group does not admit a bi-Li...
• Bass' NK groups and cd h-fibrant Hochschild homology AI翻译
  作者：Cortinas, G.; Haesemeyer, C.; Walker, Mark E.; Weibel, C.
  作者单位：University of California System; University of California Los Angeles; University of Buenos Aires; University of Nebraska System; University of Nebraska Lincoln; Rutgers University System; Rutgers University New Brunswick
  摘要：The K-theory of a polynomial ring R[t] contains the K-theory of R as a summand. For R commutative and containing ae, we describe K (*)(R[t])/K (*)(R) in terms of Hochschild homology and the cohomology of Kahler differentials for the cdh topology. We use this to address Bass' question, whether K (n) (R)=K (n) (R[t]) implies K (n) (R)=K (n) (R[t (1),t (2)]). The answer to this question is affirmative when R is essentially of finite type over the complex numbers, but negative in general.
• Collapsing irreducible 3-manifolds with nontrivial fundamental group AI翻译
  作者：Bessieres, L.; Besson, G.; Boileau, M.; Maillot, S.; Porti, J.
  作者单位：Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Communaute Universite Grenoble Alpes; Universite Grenoble Alpes (UGA); Universite Federale Toulouse Midi-Pyrenees (ComUE); Universite de Toulouse; Institut National des Sciences Appliquees de Toulouse; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite Toulouse III - Paul Sabatier; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite de Montpellier; Autonomous University of Barcelona
  摘要：Let M be a closed, orientable, irreducible, non-simply connected 3-manifold. We prove that if M admits a sequence of Riemannian metrics which volume-collapses and whose sectional curvature is locally controlled, then M is a graph manifold. This is the last step in Perelman's proof of Thurston's Geometrisation Conjecture.
• Growth of balls of holomorphic sections and energy at equilibrium AI翻译
  作者：Berman, Robert; Boucksom, Sebastien
  作者单位：Centre National de la Recherche Scientifique (CNRS); Universite Paris Cite
  摘要：Let L be a big line bundle on a compact complex manifold X. Given a non-pluripolar compact subset K of X and a continuous Hermitian metric e (-phi) on L, we define the energy at equilibrium of (K,phi) as the Monge-AmpSre energy of the extremal psh weight associated to (K,phi). We prove the differentiability of the energy at equilibrium with respect to phi, and we show that this energy describes the asymptotic behaviour as k -> a of the volume of the sup-norm unit ball induced by (K,k phi) on t...
• Rates of convergence for the homogenization of fully nonlinear uniformly elliptic pde in random media AI翻译
  作者：Caffarelli, Luis A.; Souganidis, Panagiotis E.
  作者单位：University of Texas System; University of Texas Austin; University of Chicago
  摘要：We establish a logarithmic-type rate of convergence for the homogenization of fully nonlinear uniformly elliptic second-order pde in strongly mixing media with similar, i.e., logarithmic, decorrelation rate. The proof consists of two major steps. The first, which is actually the only place in the paper where probability plays a role, establishes the rate for special (quadratic) data using the methodology developed by the authors and Wang to study the homogenization of nonlinear uniformly ellip...
• Geometric invariant theory and the generalized eigenvalue problem AI翻译
  作者：Ressayre, N.
  作者单位：Universite de Montpellier
  摘要：Let G be a connected reductive subgroup of a complex connected reductive group (G) over cap. Fix maximal tori and Borel subgroups of G and (G) over cap. Consider the cone LR( G, (G) over cap) generated by the pairs (v, (v) over cap) of dominant characters such that V-v*. is a submodule of V (v) over cap. ( with usual notation). Here we give a minimal set of inequalities describing LR(G, (G) over cap) as a part of the dominant chamber. In other words, we describe the facets of LR(G, (G) over ca...
• A SierpiAski carpet with the co-Hopfian property AI翻译
  作者：Merenkov, Sergei
  作者单位：University of Illinois System; University of Illinois Urbana-Champaign
  摘要：Motivated by questions in geometric group theory we define a quasisymmetric co-Hopfian property for metric spaces and provide an example of a metric SierpiAski carpet with this property. As an application we obtain a quasi-isometrically co-Hopfian Gromov hyperbolic space with a SierpiAski carpet boundary at infinity. In addition, we give a complete description of the quasisymmetry group of the constructed SierpiAski carpet. This group is uncountable and coincides with the group of bi-Lipschitz...
• Group measure space decomposition of II1 factors and W*-superrigidity AI翻译
  作者：Popa, Sorin; Vaes, Stefaan
  作者单位：KU Leuven; University of California System; University of California Los Angeles
  摘要：We prove a unique crossed product decomposition result for group measure space II1 factors L-infinity(X) (sic) Gamma arising from arbitrary free ergodic probability measure preserving (p. m. p.) actions of groups Gamma in a fairly large family G, which contains all free products of a Kazhdan group and a non-trivial group, as well as certain amalgamated free products over an amenable subgroup. We deduce that if T-n denotes the group of upper triangular matrices in PSL(n, Z), then any free, mixi...
• On the number of zeros of Abelian integrals AI翻译
  作者：Binyamini, Gal; Novikov, Dmitry; Yakovenko, Sergei
  作者单位：Weizmann Institute of Science
  摘要：We prove that the number of limit cycles generated from nonsingular energy level ovals (periodic trajectories) in a small non-conservative perturbation of a Hamiltonian polynomial vector field on the plane, is bounded by a double exponential of the degree of the fields. This solves the long-standing infinitesimal Hilbert 16th problem. The proof uses only the fact that Abelian integrals of a given degree are horizontal sections of a regular flat meromorphic connection defined over ae (the Gauss...