Geodesic
Transportation-cost inequalities on path space over manifolds with boundary
Documenta mathematica, Tome 18 (2013), pp. 297-322
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Let L=Δ+Z for a C1 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−∇Z≥−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.
DOI : 10.4171/dm/398
Classification : 60J60
Mots-clés : second fundamental form, curvature, transportation-cost inequality, path space 
@article{10_4171_dm_398,
     author = {Feng-Yu Wang},
     title = {Transportation-cost inequalities on path space over manifolds with boundary},
     journal = {Documenta mathematica},
     pages = {297--322},
     year = {2013},
     volume = {18},
     doi = {10.4171/dm/398},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/dm/398/}
}
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Feng-Yu Wang. Transportation-cost inequalities on path space over manifolds with boundary. Documenta mathematica, Tome 18 (2013), pp. 297-322. doi: 10.4171/dm/398

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