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作者：Artstein-Avidan, Shiri; Milman, Vitali
摘要：In the main theorem of this paper we show that any involution on the class of lower semi-continuous convex functions which is order-reversing, must be, up to linear terms, the well known Legendre transform.
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作者：Levin, Aaron
摘要：We prove new theorems that are higher-dimensional generalizations of the classical theorems of Siegel on integral points on affine curves and of Picard on holomorphic maps from C to affine curves. These include results on integral points over varying number fields of bounded degree and results on Kobayashi hyperbolicity. We give a number of new conjectures describing, from our point of view, how we expect Siegel's and Picard's theorems to optimally generalize to higher dimensions.
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作者：Felix, Yves; Halperin, Steve; Thomas, Jean-Claude
摘要：Let X be an n-dimensional, finite, simply connected CW complex and set alpha(X) = lim sup(i) (log rank pi(i) (X))/i. We prove that either rank pi(i) (X) = 0, i >= 2n or else that 0 < alpha(X) < infinity and that for any epsilon > 0 there is a K = K(epsilon) such that e((alpha X - epsilon)k) <= Sigma(k+n)(i=k+2) rank pi(i) (X) <= e((alpha X + epsilon)k), for all k >= K. In particular, this sum grows exponentially in k.
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作者：Gehring, Frederick W.; Martin, Gaven J.
摘要：We identify the two minimal co-volume lattices of the isometry group of hyperbolic 3-space that contain a finite spherical triangle group. These two groups are arithmetic and are in fact the two minimal co-volume lattices. Our results here represent the key step in establishing this fact, thereby solving a problem posed by Siegel in 1945. As a consequence we obtain sharp bounds on the order of the symmetry group of a hyperbolic 3-manifold in terms of its volume, analogous to the Hurwitz 84g - ...
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作者：Pujals, Enrique R.; Sambarino, Martin
摘要：Let f : M -> M be a C-2-diffeomorphism of a compact surface. We give a complete description of the dynamics of any compact invariant set having dominated splitting. In particular, we prove a Spectral Decomposition Theorem for the limit set L(f) under the assumption of dominated splitting. Moreover, we describe all the bifurcations that these systems can exhibit and the different types of dynamics that could follow for small C-r-perturbations.
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作者：Saji, Kentaro; Umehara, Masaaki; Yamada, Kotaro
摘要：We shall introduce the singular curvature function on cuspidal edges of surfaces, which is related to the Gauss-Bonnet formula and which characterizes the shape of cuspidal edges. Moreover, it is closely related to the behavior of the Gaussian curvature of a surface near cuspidal edges and swallowtails.
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作者：Soundararajan, Kannan
摘要：Assuming the Riemann hypothesis, we obtain an upper bound for the moments of the Riemann zeta function on the critical line. Our bound is nearly as sharp as the conjectured asymptotic formulae for these moments. The method extends to moments in other families of L-functions.
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作者：Fefferman, Charles
摘要：Fix m, n >= 1. Given an N-point set E subset of R-n, we exhibit a list of O(N) subsets S-1, S-2,..., S-L subset of E, each containing O(1) points, such that the following holds: Let f : E -> R-n. Suppose that, for each l = 1,..., L, there exists F-l is an element of C-m (R-n) with norm <= 1, agreeing with f on S-l. Then there exists F is an element of C-m (R-n), with norm O (1), agreeing with f on E. We give an application to the problem of discarding outliers from the set E.
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作者：Schlag, W.
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作者：Goldman, William M.; Labourie, Francois; Margulis, Gregory
摘要：Let Gamma(0) subset of O(2, 1) be a Schottky group, and let Sigma = H-2/Gamma(0) be the corresponding hyperbolic surface. Let C(Sigma) denote the space of unit length geodesic currents on Sigma. The cohomology group H-1(Gamma(0), V) parametrizes equivalence classes of affine deformations Gamma(u) of Gamma(0) acting on an irreducible representation V of O(2, 1). We define a continuous biaffine map psi : C(Sigma) x H-1 (Gamma(0), V) -> R which is linear on the vector space H-1 (Gamma(0), V). An ...
