Analysis on Path Spaces over Riemmannian Manifolds with Boundary
Probability
2010-02-16 v1 Differential Geometry
Abstract
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 a integration by parts formula, which leads to the standard log-Sobolev inequality for the associated Dirichlet form on the path space.
Cite
@article{arxiv.1002.2887,
title = {Analysis on Path Spaces over Riemmannian Manifolds with Boundary},
author = {Feng-Yu Wang},
journal= {arXiv preprint arXiv:1002.2887},
year = {2010}
}
Comments
14 pages