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作者：Kahn, Jeremy; Lyubich, Mikahil
摘要：On a Riemann surface S of finite type containing a family of N disjoint disks D-i (islands), we consider several natural conformal invariants measuring the distance from the islands to partial derivative S and the separation between different islands. In a near degenerate situation we establish a relation between them called the Quasi-Additivity Law. We then generalize it to a Quasi-Invariance Law providing us with a transformation rule of the moduli in question under covering maps. This rule ...
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作者：Killip, Rowan; Simon, Barry
摘要：Necessary and sufficient conditions are presented for a positive measure to be the spectral measure of a half-line Schrodinger operator with square integrable potential.
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作者：Lubinsky, Doron S.
摘要：We show how localization and smoothing techniques can be used to establish universality in the bulk of the spectrum for a fixed positive measure mu on [-1, 1]. Assume that mu is a regular measure, and is absolutely continuous in an open interval containing some point x. Assume moreover, that mu' is positive and continuous at x. Then universality for mu holds at x. If the hypothesis holds for x in a compact subset of (-1, 1), universality holds uniformly for such x. Indeed, this follows from un...
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作者：Berndtsson, Bo
摘要：Let L be a (semi)-positive line bundle over a Kahler manifold, X, fibered over a complex manifold Y. Assuming the fibers are compact and nonsingular we prove that the hermitian vector bundle E over Y whose fibers over points y are the spaces of global sections over X-y to L circle times K-X/Y, endowed with the L-2-metric, is (semi)-positive in the sense of Nakano. We also discuss various applications, among them a partial result on a conjecture of Griffiths on the positivity of ample bundles.
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作者：Alon, Noga; Shapira, Asaf; Sudakov, Benny
摘要：A graph property is monotone if it is closed under removal of vertices and edges. In this paper we consider the following algorithmic problem, called the edge-deletion problem; given a monotone property 91 and a graph G, compute the smallest number of edge deletions that are needed in order to turn G into a graph satisfying P. We denote this quantity by E'(P)(G). The first result of this paper states that the edge-deletion problem can be efficiently approximated for any monotone property. For ...
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作者：Lott, John; Villani, Cedric
摘要：We define a notion of a measured length space X having nonnegative N-Ricci curvature, for N is an element of [1, infinity), or having infinity-Ricci curvature bounded below by K, for K is an element of R. The definitions are in terms of the displacement convexity of certain functions on the associated Wasserstein metric space P-2 (X) of probability measures. We show that these properties are preserved under measured Gromov-Hausdorff limits. We give geometric and analytic consequences.
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作者：Manolescu, Ciprian; Ozsvath, Peter; Sarkar, Sucharit
摘要：Given a grid presentation of a knot (or link) K in the three-sphere, we describe a Heegaard diagram for the knot complement in which the Heegaard surface is a torus and all elementary domains are squares. Using this diagram, we obtain a purely combinatorial description of the knot Floer homology of K.
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作者：Fayad, Bassam; Khanin, Kostantin
摘要：We show that a finite number of commuting diffeomorphisms with simultaneously Diophantine rotation numbers are smoothly conjugated to rotations. This solves a problem raised by Moser.
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作者：Fisher, David; Margulis, Gregory
摘要：Let J be a semisimple Lie group with all simple factors of real rank at least two. Let Gamma < J be a lattice. We prove a very general local rigidity result about actions of J or Gamma. This shows that almost all so-called standard actions are locally rigid. As a special case, we see that any action of Gamma by toral automorphisms is locally rigid. More generally, given a manifold M on which Gamma acts isometrically and a torus T-n on which it acts by automorphisms, we show that the diagonal a...
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作者：Cohn, Henry; Kumar, Abhinav
摘要：We prove that the Leech lattice is the unique densest lattice in R-24. The proof combines human reasoning with computer verification of the properties of certain explicit polynomials. We furthermore prove that no sphere packing in R-24 can exceed the Leech lattice's density by a factor of more than 1 + 1.65 . 10(-30), and we give a new proof that E-8 is the unique densest lattice in R-8.
