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作者：Lindenstrauss, E; Meiri, D; Peres, Y
摘要：Given ergodic p-invariant measures {mu(i)} on the 1-torus T = R/Z, we give a sharp condition on their entropies, guaranteeing that the entropy of the convolution mu(1) *...* mu(n) converges to log p. We also prove a variant of this result for joinings of full entropy on T-N. In conjunction with a method of Host, this yields the following. Denote sigma(q)(x) = qx (mod 1). Then for every p-invariant ergodic mu with positive entropy, 1/N Sigma(n=0)(N-1) sigma(cn)mu converges weak* to Lebesgue mea...
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作者：Brudnyi, A
摘要：The main objective of this paper is to prove a new inequality for plurisubharmonic functions estimating their supremum over a ball by their supremum over a measurable subset of the ball. We apply this result to study local properties of polynomial, algebraic and analytic functions. The paper has much in common with an earlier paper [Br] of the author.
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作者：Gardner, RJ; Koldobsky, A; Schlumprecht, T
摘要：We derive a formula connecting the derivatives of parallel section functions of an origin-symmetric star body in R-n with the Fourier transform of powers of the radial function of the body. A parallel section function (or (n - 1)-dimensional X-ray) gives the ((n - 1)-dimensional) volumes of all hyperplane sections of the body orthogonal to a given direction. This formula provides a new characterization of intersection bodies in R-n and leads to a unified analytic solution to the Busemann-Petty...
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作者：Lacey, M; Thiele, C
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作者：Keel, S
摘要：A necessary and sufficient condition is given for semi-ampleness of a numerically effective (nef) and big line bundle in positive characteristic. One application is to the geometry of the universal stable curve over (M) over bar(g), specifically, the semi-ampleness of the relative dualizing sheaf, ill positive characteristic. An example is given which shows this and the semi-ampleness criterion fail in characteristic zero. A second application is to Mori's program for minimal models of 3-folds...
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作者：Schueth, D
摘要：We construct continuous families of Riemannian metrics on certain simply connected manifolds with the property that the resulting Riemannian manifolds are pairwise isospectral for the Laplace operator acting on functions. These are the first examples of simply connected Riemannian manifolds without boundary which are isospectral, but not isometric. For example, Ne construct continuous isospectral families of metrics on the product of spheres S-4 x S-3 x S-3. The metrics considered are not loca...
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作者：Putinar, M; Vasilescu, FH
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作者：Bentkus, V; Götze, F
摘要：For d-dimensional irrational ellipsoids E with d greater than or equal to 9 we show that the number of lattice points in rE is approximated by the volume of rE, as r tends to infinity, up to an error of order o(r(d-2)). The estimate refines an earlier authors' bound of order o(r(d-2)) which holds for arbitrary ellipsoids, and is optimal for rational ellipsoids. As an application we prove a conjecture of Davenport and Lewis that the gaps between successive values, say s < n(s), s, n(s) E Q[Zd],...
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作者：Kaloshin, VY
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作者：Barreira, L; Pesin, Y; Schmeling, J
摘要：We prove that every hyperbolic measure invariant under a C1+alpha diffeomorphism of a smooth Riemannian manifold possesses asymptotically almost local product structure, i.e., its density can be approximated by the product of the densities on stable and unstable manifolds up to small exponentials. This has not been known even for measures supported on locally maximal hyperbolic sets. Using this property of hyperbolic measures we prove the long-standing Eckmann-Ruelle conjecture in dimension th...
