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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:

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Authors and Affiliations

  1. Department of Mathematics, Northwestern University, Evanston, IL 60208, USA.¶E-mail: elton@math.nwu.edu, , , , , , US

    Elton P. Hsu

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  1. Elton P. Hsu
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Received: 3 September 1996 / Accepted: 6 February 1997

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Hsu, E. Logarithmic Sobolev Inequalities on Path Spaces Over Riemannian Manifolds . Comm Math Phys 189, 9–16 (1997). https://doi.org/10.1007/s002200050188

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  • DOI: https://doi.org/10.1007/s002200050188

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