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Super-Ricci flows and improved gradient and transport estimates

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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.)

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Correspondence to Eva Kopfer.

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Kopfer, E. Super-Ricci flows and improved gradient and transport estimates. Probab. Theory Relat. Fields 175, 897–936 (2019).

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