Gradient flows for semiconvex functions on metric measure spaces – existence, uniqueness, and Lipschitz continuity
| Autor: | Karl-Theodor Sturm |
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| Rok vydání: | 2018 |
| Předmět: |
Pure mathematics
Applied Mathematics General Mathematics 010102 general mathematics Metric Geometry (math.MG) Space (mathematics) Lipschitz continuity 01 natural sciences Measure (mathematics) Upper and lower bounds Mathematics - Metric Geometry Flow (mathematics) Bounded function 0103 physical sciences FOS: Mathematics Mathematics::Metric Geometry Mathematics::Differential Geometry 010307 mathematical physics Uniqueness 0101 mathematics Ricci curvature Mathematics |
| Zdroj: | Proceedings of the American Mathematical Society |
| ISSN: | 1088-6826 0002-9939 |
| DOI: | 10.1090/proc/14061 |
| Popis: | Given any continuous, lower bounded and $\kappa$-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 $d(x_t,x'_t)\le e^{-\kappa\, t} d(x_0,x_0').$ Comment: to appear in Proc. AMS |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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