Geodesic
Transportation-cost inequalities on path space over manifolds with boundary
Documenta mathematica, Tome 18 (2013), pp. 297-322.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

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.
Classification : 60J60, 58G60
Keywords: transportation-cost inequality, curvature, second fundamental form, path space 
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     author = {Wang, Feng-Yu},
     title = {Transportation-cost inequalities on path space over manifolds with boundary},
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     year = {2013},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/DOCMA_2013__18__a40/}
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Wang, Feng-Yu. Transportation-cost inequalities on path space over manifolds with boundary. Documenta mathematica, Tome 18 (2013), pp. 297-322. http://geodesic.mathdoc.fr/item/DOCMA_2013__18__a40/