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作者：Dinh, TC; Sibony, N
摘要：Let X be a complex projective manifold and let f be a dominating rational map from X onto X. We show that the topological entropy h(f) of f is bounded from above by the logarithm of its maximal dynamical degree.
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作者：Avila, A; Moreira, CG
摘要：We prove that almost every nonregular real quadratic map is Collet-Eckmann and has polynomial recurrence of the critical orbit (proving a conjecture by Sinai). It follows that typical quadratic maps have excellent ergodic properties, as exponential decay of correlations (Keller and Nowicki, Young) and stochastic stability in the strong sense (Baladi and Viana). This is an important step in achieving the same results for more general families of unimodal maps.
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作者：Pestov, L; Uhlmann, G
摘要：We prove that knowing the lengths of geodesics joining points of the boundary of a two-dimensional, compact, simple Riemannian manifold with boundary, we can determine uniquely the Riemannian metric up to the natural obstruction.
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作者：Tolsa, X
摘要：Let phi : C -> C be a bilipschitz map. We prove that if E c C is compact, and gamma(E), alpha(E) stand for its analytic and continuous analytic capacity respectively, then C-1 gamma(E) <= gamma(phi(E)) <= C gamma(E) and C-1 alpha(E) <= alpha(phi(E)) <= C alpha(E), where C depends only on the bilipschitz constant of phi. Further, we show that if mu is a Radon measure on C and the Cauchy transform is bounded on L-2(,U), then the Cauchy transform is also bounded on L-2(phi#mu), where phi#mu is th...
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作者：Hassell, A; Wunsch, J
摘要：Let g be a scattering metric on a compact manifold X with boundary, i.e., a smooth metric giving the interior X degrees the structure of a complete Riemannian manifold with asymptotically conic ends. An example is any compactly supported perturbation of the standard metric on R-n. Consider the operator H = 1/2 Delta + V, where Delta is the positive Laplacian with respect to g and V is a smooth real-valued function on X vanishing to second order at partial derivative X. Assuming that g is nontr...
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作者：Meeks, WH III; Rosenberg, H
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作者：Stolovitch, L
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作者：Kedlaya, KS
摘要：We produce a canonical filtration for locally free sheaves on an open p-adic annulus equipped with a Frobenius structure. Using this filtration, we deduce a conjecture of Crew on p-adic differential equations, analogous to Grothendieck's local monodromy theorem (also a consequence of results of Andre and of Mebkhout). Namely, given a finite locally free sheaf on an open p-adic annulus with a connection and a compatible Frobenius structure, the module admits a basis over a finite cover of the a...
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作者：Bismut, JM; Goette, S
摘要：The purpose of this paper is to give an explicit local formula for the difference of two natural versions of equivariant analytic torsion in de Rham theory. This difference is the sum of the integral of a Chern-Simons current and of a new invariant, the V-invariant of an odd dimensional manifold equipped with an action of a compact Lie group. The V-invariant localizes on the critical manifolds of invariant Morse-Bott functions. The results in this paper are shown to be compatible with results ...
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作者：Yau, HT
摘要：We prove that the diffusion coefficient for the two dimensional asymmetric simple exclusion process with nearest-neighbor-jumps diverges as (log t)(2/3) to the leading order. The method applies to nearest and non-nearest neighbor asymmetric simple exclusion processes.
