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• W1167736825 abstract "Let Lt:=Δt+Zt for a C1,1-vector field Z on a differential manifold M possibly with a boundary ∂M, where Δt is the Laplacian operator induced by a time dependent metric gt differentiable in t∈[0,Tc). In this article, by constructing suitable coupling, transportation-cost inequalities on the path space of the (reflecting if ∂M≠∅) diffusion process generated by Lt 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." @default.
• W1167736825 created "2016-06-24" @default.
• W1167736825 creator A5005068593 @default.
• W1167736825 date "2016-06-01" @default.
• W1167736825 modified "2023-09-30" @default.
• W1167736825 title "Transportation-cost inequalities on path spaces over manifolds carrying geometric flows" @default.
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• W1167736825 doi "https://doi.org/10.1016/j.bulsci.2015.08.001" @default.
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