-
作者：Markovic, Vladimir
作者单位：California Institute of Technology
摘要：We prove that a quasiconformal map of the sphere S-2 admits a harmonic quasi-isometric extension to the hyperbolic space H-3, thus confirming the well known Schoen Conjecture in dimension 3.
-
作者：Escobedo, M.; Velazquez, J. J. L.
作者单位：University of Basque Country; Basque Center for Applied Mathematics (BCAM); University of Bonn
摘要：The homogeneous bosonic Nordheim equation is a kinetic equation describing the dynamics of the distribution of particles in the space of moments for a homogeneous, weakly interacting, quantum gas of bosons. We show the existence of classical solutions of the homogeneous bosonic Nordheim equation that blow up in finite time. We also prove finite time condensation for a class of weak solutions of the kinetic equation.
-
作者：Mitkovski, Mishko; Poltoratski, Alexei
作者单位：Clemson University; Texas A&M University System; Texas A&M University College Station
摘要：We study the general moment problem for measures on the real line, with polynomials replaced by more general spaces of entire functions. As a particular case, we describe measures that are uniquely determined by a restriction of their Fourier transform to a finite interval. We apply our results to prove an extension of a theorem by Eremenko and Novikov on the frequency of oscillations of measures with a spectral gap (high-pass signals) near infinity.
-
作者：Chang, Huai-Liang; Li, Jun; Li, Wei-Ping
作者单位：Hong Kong University of Science & Technology; Fudan University; Stanford University
摘要：For a Landau-Ginzburg space , we construct Witten's top Chern class as an algebraic cycle using cosection localized virtual cycles in the case where all sectors are narrow, verify all axioms of this class, and derive an explicit formula for it in the free case. We prove that this construction is equivalent to the constructions of Polishchuk-Vaintrob, Chiodo, and Fan-Jarvis-Ruan.
-
作者：Losev, Ivan
作者单位：Northeastern University
摘要：The main goal of this paper is to compute two related numerical invariants of a primitive ideal in the universal enveloping algebra of a semisimple Lie algebra. The first one, very classical, is the Goldie rank of an ideal. The second one is the dimension of an irreducible module corresponding to this ideal over an appropriate finite W-algebra. We concentrate on the integral central character case. We prove, modulo a conjecture, that in this case the two are equal. Our conjecture asserts that ...
-
作者：Langer, Adrian
作者单位：University of Warsaw
摘要：We prove Bogomolov's inequality for Higgs sheaves on varieties in positive characteristic p that can be lifted modulo p(2). This implies the Miyaoka-Yau inequality on surfaces of non-negative Kodaira dimension liftable modulo p(2). This result is a strong version of Shepherd-Barron's conjecture. Our inequality also gives the first algebraic proof of Bogomolov's inequality for Higgs sheaves in characteristic zero, solving the problem posed by Narasimhan.
-
作者：Szekelyhidi, Gabor
作者单位：University of Notre Dame
摘要：This is a continuation of the work of Arezzo-Pacard-Singer and the author on blowups of extremal Kahler manifolds. We prove the conjecture stated in Sz,kelyhidi (Duke Math J 161(8):1411-1453, 2012), and we relate this result to the K-stability of blown up manifolds. As an application we prove that if a Kahler manifold of dimension 2 admits a constant scalar curvature (cscK) metric, then the blowup of at a point admits a cscK metric if and only if it is K-stable, as long as the exceptional divi...
-
作者：Chung, Nhan-Phu; Li, Hanfeng
作者单位：State University of New York (SUNY) System; University at Buffalo, SUNY; Chongqing University
摘要：We give algebraic characterizations for expansiveness of algebraic actions of countable groups. The notion of p-expansiveness is introduced for algebraic actions, and we show that for countable amenable groups, a finitely presented algebraic action is 1-expansive exactly when it has finite entropy. We also study the local entropy theory for actions of countable amenable groups on compact groups by automorphisms, and show that the IE group determines the Pinsker factor for such actions. For an ...
-
作者：Straube, Emil J.; Zeytuncu, Yunus E.
作者单位：Texas A&M University System; Texas A&M University College Station; University of Michigan System; University of Michigan
-
作者：Adiprasito, Karim A.; Ziegler, Guenter M.
作者单位：Universite Paris Saclay; Free University of Berlin
摘要：We construct an infinite family of 4-polytopes whose realization spaces have dimension smaller or equal to 96. This in particular settles a problem going back to Legendre and Steinitz: whether and how the dimension of the realization space of a polytope is determined/bounded by its f-vector. From this, we derive an infinite family of combinatorially distinct 69-dimensional polytopes whose realization is unique up to projective transformation. This answers a problem posed by Perles and Shephard...
