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作者：Bartels, Arthur; Lueck, Wolfgang
摘要：We prove the Borel Conjecture for a class of groups containing word-hyperbolic groups and groups acting properly, isometrically and cocompactly on a finite-dimensional CAT(0)-space.
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作者：Eskin, Alex; Fisher, David; Whyte, Kevin
摘要：In this paper, we prove that certain spaces are not quasi-isometric to Cayley graphs of finitely generated groups. In particular, we answer a question of Woess and prove a conjecture of Diestel and Leader by showing that certain homogeneous graphs are not quasi-isometric to a Cayley graph of a finitely generated group. This paper is the first in a sequence of papers proving results announced in our 2007 article Quasi-isometries and rigidity of solvable groups. In particular, this paper contain...
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作者：Serra, Enrico; Tilli, Paolo
摘要：We prove a conjecture by De Giorgi, which states that global weak solutions of nonlinear wave equations such as square w + |w|(p-2)w = 0 can be obtained as limits of functions that minimize suitable functionals of the calculus of variations. These functionals, which are integrals in space-time of a convex Lagrangian, contain an exponential weight with a parameter epsilon, and the initial data of the wave equation serve as boundary conditions. As epsilon tends to zero, the minimizers v(epsilon)...
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作者：Walsh, Miguel N.
摘要：We show that multiple polynomial ergodic averages arising from nilpotent groups of measure preserving transformations of a probability space always converge in the L-2 norm.
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作者：de la Breteche, Regis; Browning, Tim; Peyre, Emmanuel
摘要：The Manin conjecture is established for Chatelet surfaces over Q arising as minimal proper smooth models of the surface Y-2 + Z(2) = f(X) in where f is an element of Z[X] is a totally reducible polynomial of degree 3 without repeated roots. These surfaces do not satisfy weak approximation.
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作者：Paul, Sean Timothy
摘要：Let X-n -> P-N be a smooth, linearly normal algebraic variety. It is shown that the Mabuchi energy of (X, omega(FS vertical bar X)) restricted to the Bergman metrics is completely determined by the X-hyperdiscriminant of format (n - 1) and the Chow form of X. As a corollary it is shown that the Mabuchi energy is bounded from below for all degenerations in G if and only if the hyperdiscriminant polytope dominates the Chow polytope for all maximal algebraic tori H of G.
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作者：Chaudouard, Pierre-Henri; Laumon, Gerard
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作者：Lehrer, Gustav; Zhang, Ruibin
摘要：Let V = C-n be endowed with an orthogonal form and G = O(V) be the corresponding orthogonal group. Brauer showed in 1937 that there is a surjective homomorphism nu : B-r(n) -> End(G)(V-circle times r), where B-r(n) is the r-string Brauer algebra with parameter n. However the kernel of nu has remained elusive. In this paper we show that, in analogy with the case of GL(V), for r >= n+1, nu has kernel which is generated by a single idempotent element E, and we give a simple explicit formula for E...
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作者：Hytonen, Tuomas P.
摘要：For a general Calderon Zygmund operator T on RN, it is shown that parallel to T f parallel to(L2(w)) <= C(T) . sup(Q)(f(Q) w . f(Q) w(-1)) .parallel to f parallel to(L2(w)) for all Muckenhoupt weights w is an element of A(2). This optimal estimate was known as the A(2) conjecture. A recent result of Perez-Treil-Volberg reduced the problem to a testing condition on indicator functions, which is verified in this paper. The proof consists of the following elements: (i) a variant of the Nazarov-Tr...
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作者：Berczi, Gergely; Szenes, Andras
摘要：We prove a formula for Thom polynomials of A(d) singularities in any codimension. We use a combination of the test-curve model of Porteous, and the localization methods in equivariant cohomology. Our formulas are independent of the codimension, and are computationally effective up to d = 6.
