ANALYSIS ON PATH SPACES OVER RIEMANNIAN MANIFOLDS WITH BOUNDARY

摘要

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.