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∥.
Original language | English (US) |
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Pages (from-to) | 9-16 |
Number of pages | 8 |
Journal | Communications in Mathematical Physics |
Volume | 189 |
Issue number | 1 |
DOIs | |
State | Published - Jan 1 1997 |
ASJC Scopus subject areas
- Statistical and Nonlinear Physics
- Mathematical Physics