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Given any continuous, lower bounded and $\kappa$-convex function $V$ on ametric measure space $(X,d,m)$ which is infinitesimally Hilbertian andsatisfies some synthetic lower bound for the Ricci curvature in the sense ofLott-Sturm-Villani, we prove existence and uniqueness for the (downward)gradient flow for $V$. Moreover, we prove Lipschitz continuity of the floww.r.t. the starting point $d(x_t,x'_t)\le e^{-\kappa\, t} d(x_0,x_0').$

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