Communications in Mathematical Physics

, Volume 189, Issue 1, pp 9–16

Logarithmic Sobolev Inequalities on Path Spaces Over Riemannian Manifolds

  • Elton P. Hsu

DOI: 10.1007/s002200050188

Cite this article as:
Hsu, E. Comm Math Phys (1997) 189: 9. doi:10.1007/s002200050188


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:

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