Gradient Flows for Semiconvex Functions on Metric Measure Spaces - Existence, Uniqueness and Lipschitz Continuity

2014/10/15 by Sturm, Karl-Theodor · 1 citation
#FOS: Mathematics #Metric Geometry (math.MG)

paper · doi:10.48550/arxiv.1410.3966

Abstract

Given any continuous, lower bounded and κ-convex function V on a metric measure space (X,d,m) which is infinitesimally Hilbertian and satisfies some synthetic lower bound for the Ricci curvature in the sense of Lott-Sturm-Villani, we prove existence and uniqueness for the (downward) gradient flow for V. Moreover, we prove Lipschitz continuity of the flow w.r.t. the starting point d(x_t,x'_t)≤ e^{-κ t} d(x₀,x₀').

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