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作者：Maz'ya, VG; Verbitsky, IE
作者单位：University System of Ohio; Ohio State University; University of Liverpool; University of Missouri System; University of Missouri Columbia
摘要：We give explicit analytic criteria for two problems associated with the Schrodinger operator H = -Delta + Q on L-2(R-n) where Q is an element of D'(R-n) is an arbitrary real- or complex-valued potential. First, we obtain necessary and sufficient conditions on Q so that the quadratic form < Q(.), (.)> has zero relative bound with respect to the Laplacian. For Q is an element of L-loc(1)(R-n), this property can be expressed in the form of the integral inequality: vertical bar integral(Rn) vertic...
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作者：Kable, AC; Yukie, A
作者单位：Oklahoma State University System; Oklahoma State University - Stillwater; Tohoku University
摘要：We show that the number of quintic number fields whose discriminant does not exceed X in absolute value is bounded by a constant times X1+epsilon for any epsilon > 0. This may be compared with the conjecture that the number of such fields is asymptotic to a constant times X as X tends to infinity.
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作者：Liebeck, MW; Shalev, A
作者单位：Imperial College London; Hebrew University of Jerusalem
摘要：Let Gamma be a Fuchsian group of genus at least 2 (at least 3 if Gamma is non-oriented). We study the spaces of homomorphisms from Gamma to finite simple groups G, and derive a number of applications concerning random generation and representation varieties. Precise asymptotic estimates for |Hom(Gamma, G)| are given, implying in particular that as the rank of G tends to infinity, this is of the form |G|(mu(Gamma)+ 1+ o(1)), where mu(Gamma) is the measure of G. We then prove that a randomly cho...
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作者：Favre, C; Jonsson, M
作者单位：Centre National de la Recherche Scientifique (CNRS); Universite Paris Cite; University of Michigan System; University of Michigan; Royal Institute of Technology
摘要：We show that valuations on the ring R of holomorphic germs in dimension 2 may be naturally evaluated on plurisubharmonic functions, giving rise to generalized Lelong numbers in the sense of Demailly. Any plurisubharmonic function thus defines a real-valued function on the set V of valuations on R and - by way of a natural Laplace operator defined in terms of the tree structure on V - a positive measure on V. This measure contains a great deal of information on the singularity at the origin. Un...
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作者：Colliot-Thélène, JL
作者单位：Universite Paris Saclay; Centre National de la Recherche Scientifique (CNRS)
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作者：Chan, D; Ingalls, C
作者单位：University of New South Wales Sydney; University of New Brunswick
摘要：We develop the minimal model program for orders over surfaces and so establish a noncommutative generalisation of the existence and uniqueness of minimal algebraic surfaces. We define terminal orders and show that they have unique etale local structures. This shows that they are determined up to Morita equivalence by their centre and algebra of quotients. This reduces our problem to the study of pairs (Z,alpha) consisting of a surface Z and an element alpha of the Brauer group Brk(Z). We then ...
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作者：Dai, XZ; Wang, XD; Wei, GF
作者单位：University of California System; University of California Santa Barbara; Massachusetts Institute of Technology (MIT)
摘要：Inspired by the recent work [HHM03], we prove two stability results for compact Riemannian manifolds with nonzero parallel spinors. Our first result says that Ricci flat metrics which also admit nonzero parallel spinors are stable (in the direction of changes in conformal structures) as the critical points of the total scalar curvature functional. Our second result, which is a local version of the first one, shows that any metric of positive scalar curvature cannot lie too close to a metric wi...
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作者：Kerr, D; Li, HF
作者单位：Texas A&M University System; Texas A&M University College Station; University of Tokyo; University of Toronto
摘要：We introduce a version of Voiculescu-Brown approximation entropy for isometric automorphisms of Banach spaces and develop within this framework the connection between dynamics and the local theory of Banach spaces as discovered by Glasner and Weiss. Our fundamental result concerning this contractive approximation entropy, or CA entropy, characterizes the occurrence of positive values both geometrically and topologically. This leads to various applications; for example, we obtain a geometric de...
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作者：Junge, M
作者单位：University of Illinois System; University of Illinois Urbana-Champaign
摘要：We use Voiculescu's concept of free probability to construct a completely isomorphic embedding of the operator space OH in the predual of a von Neumann algebra. We analyze the properties of this embedding and determine the operator space projection constant of OHn: 108(1) root 1 + ln(n) n (<=) P: B(l(2)) --> OHninf, P-2 = P parallel to P parallel to(cb) <= 288 pi root 1 + ln(2n) n. The lower estimate is a recent result of Pisier and Shlyakhtenko that improves an estimate of order 1/(1+ ln n) o...
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作者：Buzzard, GT; Hruska, SL; Ilyashenko, Y
作者单位：Purdue University System; Purdue University; Cornell University; Lomonosov Moscow State University; Russian Academy of Sciences; Steklov Mathematical Institute of the Russian Academy of Sciences; Russian Academy of Sciences; Steklov Mathematical Institute of the Russian Academy of Sciences
摘要：A map is Kupka-Smale if all periodic points are hyperbolic and the stable and unstable manifolds of any two saddle points are transverse. Here we prove that Kupka-Smale maps form a residual set of full Lebesgue measure in the space P-d of polynomial automorphisms of C-2 of fixed dynamical degree d >= 2. We also prove that a heteroclinic point of two saddle periodic orbits may be continued over (almost) the entire parameter space for this set of maps. This is one of the first persistence theore...
