-
作者：Fei, Mingwen; Lin, Fanghua; Wang, Wei; Zhang, Zhifei
作者单位：Anhui Normal University; New York University; Zhejiang University; Peking University
摘要：In this paper, we consider the sharp interface limit of a matrix-valued Allen-Cahn equation, which takes the form: partial derivative(t)A = Delta A - epsilon(-2) (AA(T)A - A) with A: Omega subset of R-m -> R-nxn. We show that the sharp interface system is a two-phases flow system: the interface evolves according to the motion by mean curvature; in the two bulk phase regions, the solution obeys the heat flow of harmonic maps with values in O+(n) and O-(n) (represent the sets of n u n orthogonal...
-
作者：Xu, Xingwang; Ye, Jian
作者单位：Nanjing University; Chinese Academy of Sciences; Academy of Mathematics & System Sciences, CAS
摘要：This article is devoted to the study of the closed vacuum static spaces. Based on the argument of maximum principle, we show that three-dimensional closed vacuum static spaces with scalar curvature 6 must be isometric to either the standard unit sphere S-3 (1) or a finite quotient of the torus S-1 (root 1/3) x S-2 (root 1/3).
-
作者：Caro, Jerson; Pasten, Hector
作者单位：Pontificia Universidad Catolica de Chile
摘要：Building on work by Chabauty from 1941, Coleman proved in 1985 an explicit bound for the number of rational points of a curve C of genus g = 2 defined over a number field F, with Jacobian of rank at most g - 1. Namely, in the case F = Q, if p > 2g is a prime of good reduction, then the number of rational points of C is at most the number of F-p-points plus a contribution coming from the canonical class of C. We prove a result analogous to Coleman's bound in the case of a hyperbolic surface X o...
-
作者：Fournais, Soren; Solovej, Jan Philip
作者单位：Aarhus University; University of Copenhagen
摘要：For a dilute system of non-relativistic bosons in 3 dimensions inter-acting through a positive, radially symmetric, potential v with scattering length a we prove that the ground state energy density satisfies the bound e(rho) >= 4 pi a rho(2)(1+128/15 root pi root rho a(3)+o(root rho a(3))), thereby proving a lower bound consistent with the Lee-Huang-Hang formula for the energy density. The proof allows for potentials with largeL1-norm, in particular, the case of hard core interactions is incl...
-
作者：Le, Daniel; Le Hung, Bao V.; Levin, Brandon; Morra, Stefano
作者单位：Purdue University System; Purdue University; Northwestern University; Rice University; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite Paris-VIII
摘要：We construct projective varieties in mixed characteristic whose singularities model, in generic cases, those of tamely potentially crystalline Galois deformation rings for unramified extensions of Q(p) with small regular Hodge-Tate weights. We establish several significant facts about their geometry including a unibranch property at special points and a representation theoretic description of the irreducible components of their special fibers. We derive from these geometric results a number of...
-
作者：Chirivi, Rocco; Fang, Xin; Littelmann, Peter
作者单位：University of Salento; RWTH Aachen University; University of Cologne
摘要：We introduce the notion of a Seshadri stratification on an embedded projective variety. Such a structure enables us to construct a Newton-Okounkov simplicial complex and a flat degeneration of the projective variety into a union of toric varieties. We show that the Seshadri stratification provides a geometric setup for a standard monomial theory. In this framework, Lakshmibai-Seshadri paths for Schubert varieties get a geometric interpretation as successive vanishing orders of regular functions.
-
作者：Ascher, Kenneth; DeVleming, Kristin; Liu, Yuchen
作者单位：University of California System; University of California Irvine; University of Massachusetts System; University of Massachusetts Amherst; Northwestern University
摘要：We show that the K-moduli spaces of log Fano pairs (P-3, cS) where S is a quartic surface interpolate between the GIT moduli space of quartic surfaces and the Baily-Borel compactification of moduli of quartic K3 surfaces as c varies in the interval (0, 1). We completely describe the wall crossings of these K-moduli spaces. As the main application, we verify Laza-O' Grady's prediction on the Hassett-Keel-Looijenga program for quartic K3 surfaces. We also obtain the K-moduli compactification of ...
-
作者：Topley, Lewis
作者单位：University of Bath
摘要：In this paper we study the variety of one dimensional representations of a finite W algebra attached to a classical Lie algebra, giving a precise description of the dimensions of the irreducible components. We apply this to prove a conjecture of Losev describing the image of his orbit method map. In order to do so we first establish new Yangian-type presentations of semiclassical limits of the W-algebras attached to distinguished nilpotent elements in classical Lie algebras, using Dirac reduct...
-
作者：He, Qiao; Li, Chao; Shi, Yousheng; Yang, Tonghai
作者单位：University of Wisconsin System; University of Wisconsin Madison; Columbia University; Zhejiang University
摘要：We prove the Kudla-Rapoport conjecture for Kramer models of unitary Rapoport-Zink spaces at ramified places. It is a precise identity between arithmetic intersection numbers of special cycles on Kramer models and modified derived local densities of hermitian forms. As an application, we relax the local assumptions at ramified places in the arithmetic Siegel-Weil formula for unitary Shimura varieties, which is in particular applicable to unitary Shimura varieties associated to unimodular hermit...
-
作者：Labourie, Francois; Toulisse, Jeremy
作者单位：Universite Cote d'Azur; Centre National de la Recherche Scientifique (CNRS)
摘要：We study in this paper quasiperiodic maximal surfaces in pseudo-hyperbolic spaces and show that they are characterised by a curvature condition, Gromov hyperbolicity or conformal hyperbolicity. We show that the limit curves of these surfaces in the Einstein Universe admits a canonical quasisymmetric parametrisation, while conversely every quasisymmetric curve in the Einstein Universe bounds a quasiperiodic surface in such a way that the quasisymmetric parametrisation is a continuous extension ...
