Eva Kopfer Super-Ricci flows and improved gradient and transport estimates Probability Theory and Related Fields 2019 10.1007/s00440-019-00904-6
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{\$}{\$}Lp-Kantorovich distance, {\$}{\$}p{\backslash}in [1,{\backslash}infty ]{\$}{\$}pâ[1,â]. These transport estimates turn out to characterize super-Ricci flows, introduced by Sturm (J Funct Anal 275(12):3504--3569, 2015.)
2018
Matthias Erbar and Eva Kopfer Super Ricci flows for Markov chains arxiv e-print 1805.06703 2018 https://arxiv.org/abs/1805.06703
Peter Gladbach, Eva Kopfer and Jan Maas Scaling limits of discrete optimal transport arxiv e-print 1809.01092 2018 https://arxiv.org/abs/1809.01092
Eva Kopfer and Karl-Theodor Sturm Heat flow on time-dependent metric measure spaces and super-Ricci flows Comm. Pure Appl. Math., 71(12): 2500--2608 2018 10.1002/cpa.21766
Eva Kopfer Gradient flow for the Boltzmann entropy and Cheeger's energy on time-dependent metric measure spaces Calc. Var. Partial Differential Equations, 57(1): Art. 20, 40 2018 10.1007/s00526-017-1287-5