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作者：Klainerman, Sergiu; Luk, Jonathan; Rodnianski, Igor
作者单位：Princeton University; University of Pennsylvania; Massachusetts Institute of Technology (MIT)
摘要：We present a new, fully anisotropic, criterion for formation of trapped surfaces in vacuum. More precisely we provide local conditions on null data, concentrated in a neighborhood of a short null geodesic segment (possibly flat in all other directions) whose future development contains a trapped surface. This extends considerably the previous result of Christodoulou (Monographs in Mathematics. European Mathematical Society, Switzerland, 2009) which required instead a uniform condition along al...
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作者：Johnson, Mathew A.; Noble, Pascal; Rodrigues, L. Miguel; Zumbrun, Kevin
作者单位：University of Kansas; Universite Claude Bernard Lyon 1; Indiana University System; Indiana University Bloomington
摘要：We establish nonlinear stability and asymptotic behavior of traveling periodic waves of viscous conservation laws under localized perturbations or nonlocalized perturbations asymptotic to constant shifts in phase, showing that long-time behavior is governed by an associated second-order formal Whitham modulation system. A key point is to identify the way in which initial perturbations translate to initial data for this formal system, a task accomplished by detailed estimates on the linearized ...
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作者：Volberg, A.; Yuditskii, P.
作者单位：Michigan State University; Johannes Kepler University Linz
摘要：This is a small theory of non almost periodic ergodic families of Jacobi matrices with purely (however) absolutely continuous spectrum. The reason why this effect may happen is that under our axioms we found an analytic condition on the resolvent set that is responsible for (exactly equivalent to) this effect.
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作者：Corwin, Ivan; Hammond, Alan
作者单位：University of Oxford
摘要：Consider a collection of N Brownian bridges ,B-i : [- N, N] -> R, B-i(-N) = B-i(N) = 0, 1 <= i <= N, conditioned not to intersect. The edge-scaling limit of this system is obtained by taking a weak limit as N -> a of the collection of curves scaled so that the point (0,2(1/2) N) is fixed and space is squeezed, horizontally by a factor of N (2/3) and vertically by N (1/3). If a parabola is added to each of the curves of this scaling limit, an x-translation invariant process sometimes called the...
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作者：Callejas-Bedregal, R.; Morgado, M. F. Z.; Seade, J.
作者单位：Universidade Federal da Paraiba; Universidade Estadual Paulista; Universidad Nacional Autonoma de Mexico
摘要：The purpose of this work is to establish a link between the theory of Chern classes for singular varieties and the geometry of the varieties in question. Namely, we show that if Z is a hypersurface in a compact complex manifold, defined by the complex analytic space of zeroes of a reduced non-zero holomorphic section of a very ample line bundle, then its Milnor classes, regarded as elements in the Chow group of Z, determine the global L cycles of Z; and vice versa: The L cycles determine the M...
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作者：Hind, R.; Kerman, E.
作者单位：University of Notre Dame; University of Illinois System; University of Illinois Urbana-Champaign
摘要：In this paper we establish new restrictions on the symplectic embeddings of basic shapes in symplectic vector spaces. By refining an embedding technique due to Guth, we also show that they are sharp.
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作者：Shiota, Masahiro
作者单位：Nagoya University
摘要：Milnor discovered two compact polyhedra which are homeomorphic but not PL homeomorphic (a counterexample to the Hauptvermutung). He constructed the homeomorphism by a finite procedure repeated infinitely often. Informally, we call a procedure constructive if it consists of an explicit procedure that is repeated only finitely many times. In this sense, Milnor did not give a constructive procedure to define the homeomorphism between the two polyhedra. In the case where the homeomorphism is semia...
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作者：Hertz, Federico Rodriguez; Wang, Zhiren
作者单位：Pennsylvania Commonwealth System of Higher Education (PCSHE); Pennsylvania State University; Pennsylvania State University - University Park; Yale University
摘要：We show that all Anosov -actions on tori and nilmanifolds without rank-one factor actions are, up to conjugacy, actions by automorphisms.
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作者：Le Maitre, Francois
作者单位：Ecole Normale Superieure de Lyon (ENS de LYON)
摘要：We completely elucidate the relationship between two invariants associated with an ergodic probability measure-preserving (pmp) equivalence relation, namely its cost and the minimal number of topological generators of its full group. It follows that for any free pmp ergodic action of the free group on n generators, the minimal number of topological generators for the full group of the action is n + 1, answering a question of Kechris.
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作者：O'Connell, Neil; Seppalainen, Timo; Zygouras, Nikos
作者单位：University of Warwick; University of Wisconsin System; University of Wisconsin Madison; University of Warwick
摘要：We show that the geometric lifting of the RSK correspondence introduced by A.N. Kirillov (Physics and Combinatorics. Proc. Nagoya 2000 2nd Internat Workshop, pp. 82-150, 2001) is volume preserving with respect to a natural product measure on its domain, and that the integrand in Givental's integral formula for -Whittaker functions arises naturally in this context. Apart from providing further evidence that Whittaker functions are the natural analogue of Schur polynomials in this setting, our r...
