2016

最新文章

• Divisionally free arrangements of hyperplanes AI翻译
  作者：Abe, Takuro
  作者单位：Kyoto University
  摘要：Let be the triple of hyperplane arrangements. We show that the freeness of and the division of by imply the freeness of . This division theorem improves the famous addition-deletion theorem, and it has several applications, which include a definition of divisionally free arrangements. It is a strictly larger class of free arrangements than the classical important class of inductively free arrangements. Also, whether an arrangement is divisionally free or not is determined by the combinatorics....
• Representations of the Kauffman bracket skein algebra I: invariants and miraculous cancellations AI翻译
  作者：Bonahon, Francis; Wong, Helen
  作者单位：University of Southern California; Carleton College
  摘要：We study finite-dimensional representations of the Kauffman bracket skein algebra of a surface S. In particular, we construct invariants of such irreducible representations when the underlying parameter is a root of unity. The main one of these invariants is a point in the character variety consisting of group homomorphisms from the fundamental group to , or in a twisted version of this character variety. The proof relies on certain miraculous cancellations that occur for the quantum trace hom...
• K-polystability of Q-Fano varieties admitting Kahler-Einstein metrics AI翻译
  作者：Berman, Robert J.
  作者单位：Chalmers University of Technology; University of Gothenburg
  摘要：It is shown that any, possibly singular, Fano variety X admitting a Kahler-Einstein metric is K-polystable, thus confirming one direction of the Yau-Tian-Donaldson conjecture in the setting of Q-Fano varieties equipped with their anti-canonical polarization. The proof is based on a new formula expressing the Donaldson-Futaki invariants in terms of the slope of the Ding functional along a geodesic ray in the space of all bounded positively curved metrics on the anti-canonical line bundle of X. ...
• Quotients of surface groups and homology of finite covers via quantum representations AI翻译
  作者：Koberda, Thomas; Santharoubane, Ramanujan
  作者单位：University of Virginia; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite Paris Cite
  摘要：We prove that for each sufficiently complicated orientable surface S, there exists an infinite image linear representation of such that if is freely homotopic to a simple closed curve on S, then has finite order. Furthermore, we prove that given a sufficiently complicated orientable surface S, there exists a regular finite cover such that is not generated by lifts of simple closed curves on S, and we give a lower bound estimate on the index of the subgroup generated by lifts of simple closed c...
• Sharp eigenvalue bounds and minimal surfaces in the ball AI翻译
  作者：Fraser, Ailana; Schoen, Richard
  作者单位：University of British Columbia; Stanford University; University of California System; University of California Irvine
  摘要：We prove existence and regularity of metrics on a surface with boundary which maximize sigma(1) L where sigma(1) is the first nonzero Steklov eigenvalue and L the boundary length. We show that such metrics arise as the induced metrics on free boundary minimal surfaces in the unit ball B-n for some n. In the case of the annulus we prove that the unique solution to this problem is the induced metric on the critical catenoid, the unique free boundary surface of revolution in B-3. We also show tha...
• Continuity of core entropy of quadratic polynomials AI翻译
  作者：Tiozzo, Giulio
  作者单位：Yale University
  摘要：The core entropy of polynomials, recently introduced by W. Thurston, is a dynamical invariant which can be defined purely in combinatorial terms, and provides a useful tool to study parameter spaces of polynomials. The theory of core entropy extends the entropy theory for real unimodal maps to complex polynomials: the real segment is replaced by an invariant tree, known as the Hubbard tree, which lies inside the filled Julia set. We prove that the core entropy of quadratic polynomials varies c...
• Wigner measures and observability for the Schrodinger equation on the disk AI翻译
  作者：Anantharaman, Nalini; Leautaud, Matthieu; Macia, Fabricio
  作者单位：Universites de Strasbourg Etablissements Associes; Universite de Strasbourg; Universite Paris Cite; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universidad Politecnica de Madrid
  摘要：We analyse the structure of semiclassical and microlocal Wigner measures for solutions to the linear Schrodinger equation on the disk, with Dirichlet boundary conditions. Our approach links the propagation of singularities beyond geometric optics with the completely integrable nature of the billiard in the disk. We prove a structure theorem, expressing the restriction of the Wigner measures on each invariant torus in terms of second-microlocal measures. They are obtained by performing a finer ...
• Unimodular hyperbolic triangulations: circle packing and random walk AI翻译
  作者：Angel, Omer; Hutchcroft, Tom; Nachmias, Asaf; Ray, Gourab
  作者单位：University of British Columbia; Tel Aviv University; University of Cambridge
  摘要：We show that the circle packing type of a unimodular random plane triangulation is parabolic if and only if the expected degree of the root is six, if and only if the triangulation is amenable in the sense of Aldous and Lyons [1]. As a part of this, we obtain an alternative proof of the Benjamini-Schramm Recurrence Theorem [19]. Secondly, in the hyperbolic case, we prove that the random walk almost surely converges to a point in the unit circle, that the law of this limiting point has full sup...
• The singular set of mean curvature flow with generic singularities AI翻译
  作者：Colding, Tobias Holck; Minicozzi, William P., II
  作者单位：Massachusetts Institute of Technology (MIT)
  摘要：A mean curvature flow starting from a closed embedded hyper-surface in Rn+1 must develop singularities. We show that if the flow has only generic singularities, then the space-time singular set is contained in finitely many compact embedded (n - 1)-dimensional Lipschitz submanifolds plus a set of dimension at most n-2. If the initial hypersurface is mean convex, then all singularities are generic and the results apply. In R-3 and R-4, we show that for almost all times the evolving hypersurface...
• The space of stability conditions on abelian threefolds, and on some Calabi-Yau threefolds AI翻译
  作者：Bayer, Arend; Macri, Emanuele; Stellari, Paolo
  作者单位：University of Edinburgh; University of Edinburgh; Heriot Watt University; University System of Ohio; Ohio State University; Northeastern University; University of Milan
  摘要：We describe a connected component of the space of stability conditions on abelian threefolds, and on Calabi-Yau threefolds obtained as (the crepant resolution of) a finite quotient of an abelian threefold. Our proof includes the following essential steps:We simultaneously strengthen a conjecture by the first two authors and Toda, and prove that it follows from a more natural and seemingly weaker statement. This conjecture is a Bogomolov-Gieseker type inequality involving the third Chern charac...