128 citations · 197 across the 16 of their papers we have counts for
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math.AP2023★ 3 cited
Covariance-modulated optimal transport and gradient flows
Martin Burger, Matthias Erbar, Franca Hoffmann +2
We study a variant of the dynamical optimal transport problem in which the energy to be minimised is modulated by the covariance matrix of the distribution. Such transport metrics…
math.AP2021
Gradient flow formulation of diffusion equations in the Wasserstein space over a metric graph
Matthias Erbar, Dominik Forkert, Jan Maas +1
This paper contains two contributions in the study of optimal transport on metric graphs. Firstly, we prove a Benamou-Brenier formula for the Wasserstein distance, which establishe…
math.AP2016★ 5 cited
A gradient flow approach to the Boltzmann equation
Matthias Erbar
We show that the spatially homogeneous Boltzmann equation evolves as the gradient flow of the entropy with respect to a suitable geometry on the space of probability measures which…