, Volume 189, Issue 1, pp 9-16

Logarithmic Sobolev Inequalities on Path Spaces Over Riemannian Manifolds

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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 ν 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:

Received: 3 September 1996 / Accepted: 6 February 1997