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math.FA2020★ 1 cited
Tamed spaces -- Dirichlet spaces with distribution-valued Ricci bounds
Matthias Erbar, Chiara Rigoni, Karl-Theodor Sturm +1
We develop the theory of tamed spaces which are Dirichlet spaces with distribution-valued lower bounds on the Ricci curvature and investigate these from an Eulerian point of view.…
math.FA2015
Optimal transport, Cheeger energies and contractivity of dynamic transport distances in extended spaces
Luigi Ambrosio, Matthias Erbar, Giuseppe Savaré
We introduce the setting of extended metric-topological measure spaces as a general "Wiener-like" framework for optimal transport problems and nonsmooth metric analysis in infinite…
math.FA2012
Gradient flow structures for discrete porous medium equations
Matthias Erbar, Jan Maas
We consider discrete porous medium equations of the form \partial_t ρ_t = Δϕ(ρ_t), where Δis the generator of a reversible continuous time Markov chain on a finite set X, and ϕis a…