Transportation-cost inequalities on path space over manifolds with boundary
Feng-Yu Wang00875 China
Let for a vector field on a complete Riemannian manifold possibly with a boundary. A number of transportation-cost inequalities on the path space for the (reflecting) -diffusion process are proved to be equivalent to the curvature condition 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.
Cite this article
Feng-Yu Wang, Transportation-cost inequalities on path space over manifolds with boundary. Doc. Math. 18 (2013), pp. 297–322DOI 10.4171/DM/398