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# Communications in Mathematical Sciences

## Volume 9 (2011)

### Number 4

### Analysis on path spaces over Riemannian manifolds with boundary

Pages: 1203 – 1212

DOI: http://dx.doi.org/10.4310/CMS.2011.v9.n4.a14

#### Author

#### 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 an integration by parts formula, which leads to the standard log-Sobolev inequality for the associated Dirichlet form on the path space.

#### Keywords

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

#### 2010 Mathematics Subject Classification

58-xx, 60J60