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作者：Duchin, Moon; Leininger, Christopher J.; Rafi, Kasra
作者单位：University of Michigan System; University of Michigan; University of Illinois System; University of Illinois Urbana-Champaign; University of Oklahoma System; University of Oklahoma - Norman
摘要：In this paper we consider flat metrics (semi-translation structures) on surfaces of finite type. There are two main results. The first is a complete description of when a set of simple closed curves is spectrally rigid, that is, when the length vector determines a metric among the class of flat metrics. Secondly, we give an embedding into the space of geodesic currents and use this to obtain a compactification for the space of flat metrics. The geometric interpretation is that flat metrics deg...
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作者：Figalli, A.; Maggi, F.; Pratelli, A.
作者单位：University of Texas System; University of Texas Austin; University of Florence; University of Pavia
摘要：A sharp quantitative version of the anisotropic isoperimetric inequality is established, corresponding to a stability estimate for the Wulff shape of a given surface tension energy. This is achieved by exploiting mass transportation theory, especially Gromov's proof of the isoperimetric inequality and the Brenier-McCann Theorem. A sharp quantitative version of the Brunn-Minkowski inequality for convex sets is proved as a corollary.
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作者：Esnault, Helene; Mehta, Vikram
作者单位：University of Duisburg Essen; Tata Institute of Fundamental Research (TIFR)
摘要：We show that simply connected projective manifolds in characteristic p > 0 have no nontrivial stratified bundles. This gives a positive answer to a conjecture by D. Gieseker (Ann. Sc. Norm. Super. Pisa, 4 S,r. 2(1):1-31, 1975). The proof uses Hrushovski's theorem on periodic points.
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作者：Hernandez, David
作者单位：Centre National de la Recherche Scientifique (CNRS); Institut Polytechnique de Paris; Ecole Polytechnique; Universite PSL; Ecole Normale Superieure (ENS)
摘要：Let F be the category of finite-dimensional representations of an arbitrary quantum affine algebra. We prove that a tensor product S (1) aSua <...a <...a <...aSu S (N) of simple objects of F is simple if and only S (i) aSu S (j) is simple for any i < j.
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作者：Cheeger, Jeff; Kleiner, Bruce
作者单位：New York University
摘要：This is one of a series of papers on Lipschitz maps from metric spaces to L-1. Here we present the details of results which were announced in Cheeger and Kleiner (Ann. Math., 2006, to appear, arXiv:math.MG/0611954, Sect. 1.8): a new approach to the infinitesimal structure of Lipschitz maps into L-1, and, as a first application, an alternative proof of the main theorem of Cheeger and Kleiner (Ann. Math., 2006, to appear, arXiv: math. MG/0611954), that the Heisenberg group does not admit a bi-Li...
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作者：Gille, Stefan
作者单位：University of Munich
摘要：We show that the Rost nilpotence theorem is true for geometrically rational surfaces over fields of characteristic zero.
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作者：Zhang, Shou-Wu
作者单位：Columbia University
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作者：Cortinas, G.; Haesemeyer, C.; Walker, Mark E.; Weibel, C.
作者单位：University of California System; University of California Los Angeles; University of Buenos Aires; University of Nebraska System; University of Nebraska Lincoln; Rutgers University System; Rutgers University New Brunswick
摘要：The K-theory of a polynomial ring R[t] contains the K-theory of R as a summand. For R commutative and containing ae, we describe K (*)(R[t])/K (*)(R) in terms of Hochschild homology and the cohomology of Kahler differentials for the cdh topology. We use this to address Bass' question, whether K (n) (R)=K (n) (R[t]) implies K (n) (R)=K (n) (R[t (1),t (2)]). The answer to this question is affirmative when R is essentially of finite type over the complex numbers, but negative in general.
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作者：Misiolek, Gerard; Preston, Stephen C.
作者单位：University of Colorado System; University of Colorado Boulder; University of Notre Dame
摘要：We prove that exponential maps of right-invariant Sobolev H (r) metrics on a variety of diffeomorphism groups of compact manifolds are nonlinear Fredholm maps of index zero as long as r is sufficiently large. This generalizes the result of Ebin et al. (Geom. Funct. Anal. 16, 2006) for the L (2) metric on the group of volume-preserving diffeomorphisms important in hydrodynamics. In particular, our results apply to many other equations of interest in mathematical physics. We also prove an infini...
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作者：Han, Zheng-Chao; Li, YanYan; Teixeira, Eduardo V.
作者单位：Rutgers University System; Rutgers University New Brunswick; Universidade Federal do Ceara
摘要：sigma (k) -Yamabe equations are conformally invariant equations generalizing the classical Yamabe equation. In (J. Funct. Anal. 233: 380-425, 2006) YanYan Li proved that an admissible solution with an isolated singularity at 0aae (n) to the sigma (k) -Yamabe equation is asymptotically radially symmetric. In this work we prove that such a solution is asymptotic to a radial solution to the same equation on ae (n) a-{0}. These results generalize earlier pioneering work in this direction on the cl...
