Logarithmic Sobolev inequalities on path spaces over Riemannian manifolds

被引：40

作者：

Hsu, EP

机构：

[1] Department of Mathematics, Northwestern University, Evanston

来源：

COMMUNICATIONS IN MATHEMATICAL PHYSICS | 1997年 / 189卷 / 01期

关键词：

Manifold; Brownian Motion; Riemannian Manifold; Sobolev Inequality; Ricci Curvature;

D O I：

10.1007/s002200050188

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

Let W-0(M) be the space of paths of unit time length on a connected, complete Riemannian manifold M such that gamma(0) = 0, a fixed point on M, and v the Wiener measure on W,(M) (the law of Brownian motion on M starting at 0). If the Ricci curvature is bounded by c, then the following logarithmic Sobolev inequality holds: integral(W0(M)) F-2 log \ F \ dv less than or equal to e(3c)parallel to DF parallel to(2) + parallel to F parallel to(2)log parallel to F parallel to.

引用

页码：9 / 16

页数：8

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