Communications in Mathematical Sciences

Volume 9 (2011)

Number 4

Analysis on path spaces over Riemannian manifolds with boundary

Pages: 1203 – 1212



Feng-Yu Wang (School of Mathematical Sciences, Beijing Normal University, Beijing, China)


By using Hsu’s multiplicative functional for the Neumann heat equation, a natural damped gradient operator is defined for the reflecting Brownian motion on compact manifolds with boundary. This operator is linked to quasi-invariant flows in terms of an integration by parts formula, which leads to the standard log-Sobolev inequality for the associated Dirichlet form on the path space.


log-Sobolev inequality, integration by parts formula, path space over manifolds with boundary, reflecting Brownian motion

2010 Mathematics Subject Classification

58-xx, 60J60

Published 29 July 2011