Wang, Feng-Yu

Transportation-cost inequalities on path space over manifolds with boundary

Doc. Math., J. DMV 18, 297-322 (2013)


Summary: Let $L=\Delta + Z$ for a $C^1$ vector field $Z$ on a complete Riemannian manifold possibly with a boundary. A number of transportation-cost inequalities on the path space for the (reflecting) $L$-diffusion process are proved to be equivalent to the curvature condition ${Ric}-\nabla Z\ge - K$ and the convexity of the boundary (if exists). These inequalities are new even for manifolds without boundary, and are partly extended to non-convex manifolds by using a conformal change of metric which makes the boundary from non-convex to convex.

Mathematics Subject Classification

60J60, 58G60


transportation-cost inequality, curvature, second fundamental form, path space