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An integration by parts formula on path space over manifolds carrying geometric flow

Research paper by LiJuan Cheng

Indexed on: 22 Jan '15Published on: 22 Jan '15Published in: Science China Mathematics



Abstract

We establish an integration by parts formula on the path space with reference measure ℙ, the law of the (reflecting) diffusion process on manifolds with possible boundary carrying geometric flow, which leads to the standard log-Sobolev inequality for the associated Dirichlet form. To this end, we first modify Hsu’s multiplicative functionals to define the damp gradient operator, which links to quasi-invariant flows; and then establish the derivative formula for the associated inhomogeneous diffusion semigroup.