Logarithmic sobolev inequalities on path spaces over riemannian manifolds

Elton P. Hsu

doi:10.1007/s002200050188

Logarithmic sobolev inequalities on path spaces over riemannian manifolds

Elton P. Hsu^*

^*Corresponding author for this work

Mathematics

Research output: Contribution to journal › Article › peer-review

36 Scopus citations

Abstract

Let W_o(M) be the space of paths of unit time length on a connected, complete Riemannian manifold M such that γ(0) = o, a fixed point on M, and v the Wiener measure on W_o(M) (the law of Brownian motion on M starting at o). If the Ricci curvature is bounded by c, then the following logarithmic Sobolev inequality holds: ∫_Wo(M) F² log |F|dv ≤ e^3c∥DF∥² + ∥F∥² log ∥F∥.

Original language	English (US)
Pages (from-to)	9-16
Number of pages	8
Journal	Communications in Mathematical Physics
Volume	189
Issue number	1
DOIs	https://doi.org/10.1007/s002200050188
State	Published - Jan 1 1997

ASJC Scopus subject areas

Statistical and Nonlinear Physics
Mathematical Physics

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abstract = "Let Wo(M) be the space of paths of unit time length on a connected, complete Riemannian manifold M such that γ(0) = o, a fixed point on M, and v the Wiener measure on Wo(M) (the law of Brownian motion on M starting at o). If the Ricci curvature is bounded by c, then the following logarithmic Sobolev inequality holds: ∫Wo(M) F2 log |F|dv ≤ e3c∥DF∥2 + ∥F∥2 log ∥F∥.",

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AB - Let Wo(M) be the space of paths of unit time length on a connected, complete Riemannian manifold M such that γ(0) = o, a fixed point on M, and v the Wiener measure on Wo(M) (the law of Brownian motion on M starting at o). If the Ricci curvature is bounded by c, then the following logarithmic Sobolev inequality holds: ∫Wo(M) F2 log |F|dv ≤ e3c∥DF∥2 + ∥F∥2 log ∥F∥.

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Logarithmic sobolev inequalities on path spaces over riemannian manifolds

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