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Probability Theory and Related Fields

, Volume 175, Issue 3–4, pp 897–936 | Cite as

Super-Ricci flows and improved gradient and transport estimates

  • Eva KopferEmail author
Article

Abstract

We introduce Brownian motions on time-dependent metric measure spaces, proving their existence and uniqueness. We prove contraction estimates for their trajectories assuming that the time-dependent heat flow satisfies transport estimates with respect to every \(L^p\)-Kantorovich distance, \(p\in [1,\infty ]\). These transport estimates turn out to characterize super-Ricci flows, introduced by Sturm (J Funct Anal 275(12):3504–3569, 2015.)

Mathematics Subject Classification

30L99 53C44 60J25 

Notes

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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Institut für Angewandte MathematikUniversität BonnBonnGermany

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