Communications in Mathematical Physics

, Volume 189, Issue 1, pp 9–16 | Cite as

Logarithmic Sobolev Inequalities on Path Spaces Over Riemannian Manifolds

  • Elton P. Hsu

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 ν 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:
$$$$

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Copyright information

© Springer-Verlag Berlin Heidelberg 1997

Authors and Affiliations

  • Elton P. Hsu
    • 1
  1. 1.Department of Mathematics, Northwestern University, Evanston, IL 60208, USA.¶E-mail: elton@math.nwu.eduUS

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