Reference : Transportation-cost inequalities on path spaces over manifolds carrying geometric flows
Scientific journals : Article
Physical, chemical, mathematical & earth Sciences : Mathematics
http://hdl.handle.net/10993/22982
Transportation-cost inequalities on path spaces over manifolds carrying geometric flows
English
Cheng, Li Juan mailto [University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit >]
May-2016
Bulletin des Sciences Mathématiques
Gauthier-Villars
140
5
541-561
Yes (verified by ORBilu)
International
0007-4497
Paris
France
[en] Geometric flow ; Ricci flow ; transportation-cost inequality
[en] Let Lt:=Δt+ZtLt:=Δt+Zt for a C1,1C1,1-vector field Z on a differential manifold M possibly with a boundary ∂M , where ΔtΔt is the Laplacian operator induced by a time dependent metric gtgt differentiable in t∈[0,Tc)t∈[0,Tc). In this article, by constructing suitable coupling, transportation-cost inequalities on the path space of the (reflecting if ∂M≠∅∂M≠∅) diffusion process generated by LtLt are proved to be equivalent to a new curvature lower bound condition and the convexity of the geometric flow (i.e., the boundary keeps convex). Some of them are further extended to non-convex flows by using conformal changes of the flows. As an application, these results are applied to the Ricci flow with the umbilic boundary.
National de la Recherche Luxembourg
http://hdl.handle.net/10993/22982

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