skip to main contentskip to main menuskip to footer Universität Bielefeld Play Search
  • AG Erbar


    © Universität Bielefeld



Link to existing publications on MathSciNet

Link to existing e-prints on arXiv

Google Scholar profile



  • Optimal transport of stationary point processes: Metric structure, gradient flow and convexity of the specific entropy
    with Martin Huesmann, Jonas Jalowy, and Bastian Müller
    arXiv:2304.11145, 2023. 

  • Covariance-modulated optimal transport and gradient flows
    with Martin Burger, Franca Hoffmann, Daniel Matthes and Andre Schlichting

  • Approximation of Splines in Wasserstein Spaces
    with Jorge Justiniano and Martin Rumpf

Published/Accepted Research Articles:

  • Gradient flow formulation of diffusion equations in the Wasserstein
     space over a metric graph

    with Dominik Forkert, Jan Mass and Delio Mugnolo
    Netw. Heterog. Media 17, no. 5, 687–717, (2022).

  • Tamed spaces - Dirichlet spaces with distribution-valued Ricci bounds
    with Chiara Rigoni, Karl-Theodor Sturm and Luca Tamanini
    J. Math. Pures Appl. (9) 161, (2022).

  • A gradient flow approach to the Boltzmann equation
    to appear in J. Eur. Math. Soc.

  • Entropic curvature and convergence to equilibrium for mean-field dynamics on discrete spaces
    with Max Fathi and André Schlichting
     ALEA Lat. Am. J. Probab. Math. Stat. Vol. 17, no. 1, 445--471, (2020).

  • The one-dimensional log-gas free energy has a unique minimiser
    with Martin Huesmann and Thomas Leblé
    Commun. Pure Appl. Math., 74, No. 3, 615-675 (2021).
  • Super Ricci flows for weighted graphs
    with Eva Kopfer
    J. Funct. Anal., Vol. 279, No. 6, (2020)
  • On the geometry of geodesics in discrete optimal transport
    with Jan Maas and Melchior Wirth
    Calc. Var. PDE 58:19, (2019)
  • Rigidity of cones with bounded Ricci curvature
    with Karl-Theodor Sturm
    J. Eur. Math. Soc., 23, No. 1, 219-235 (2021)

  • Computation of Optimal Transport on Discrete Metric Measure Spaces
    with Martin Rumpf, Bernhard Schmitzer and Stefan Simon,
    Numer. Math., Vol. 144, No. 1, 157--200, (2020)

  • Poincaré, modified logarithmic Sobolev and isoperimetric inequalities for Markov chains with non-negative Ricci curvature
    with Max Fathi
    J. Funct. Anal., Vol. 274, No. 11, 3056-3089, (2018)

  • Smoothing and non-smoothing via a flow tangent to the Ricci flow
    with Nicolas Juillet
    J. Math. Pures Appl., Vol. 110, 123-154, (2018)

  • Ricci bounds for weakly interacting Markov chains
    with Christopher Henderson, Georg Menz and Prasad Tetali
    Electron. J. Probab. Vol. 22, No. 40, 1-23, (2017)

  • Gradient flow structure for McKean-Vlasov equations on discrete spaces
    with Max Fathi, Vaios Laschos and Andre Schlichting
    Discrete and Continuous Dynamical Systems, 36 (12), 6799--6833, (2016)

  • Optimal transport, Cheeger energies and contractivity
    of dynamic transport distances in extended spaces

    with Luigi Ambrosio and Giuseppe Savaré
    Nonlinear Anal. Vol. 137, 77–134 (2016)

  • From large deviations to Wasserstein gradient flows in multiple dimensions
    with Jan Maas and Michiel Renger
    Electron. Commun. Probab. Vol. 20, No. 89, 1-12, (2015)

  • Ricci curvature bounds for Bernoulli-Laplace and random transposition models
    with Jan Maas and Prasad Tetali
    Ann. Fac. Sci. Toulouse Math. Vol. 24, No. 4, 781–800, (2015)

  • Curvature bounds for configuration spaces
    with Martin Huesmann
    Calc. Var. PDE, 201 (3), 397-430, (2014)

  • On the equivalence of Bochner's inequality and the entropic curvature-dimension
    condition on metric measure spaces

    with Kazumasa Kuwada and Karl-Theodor Sturm
    Invent. math. 201 (3), 993-1071, (2015)

  • Gradient flow structures for discrete porous medium equations
    with Jan Maas
    Discrete and Continuous Dynamical Systems 34 (4), 1355-1374, (2014)

  • Gradient flows of the entropy for jump processes
    Ann. Inst. H. Poincare Probab. Stat. 50 (3), 920-945, (2014)

  • Ricci curvature of finite Markov chains via convexity of the entropy
    with Jan Maas
    Arch. Rat. Mech. Anal. 206 (3), 997-1038, (2012)

  • The heat equation on manifolds as a gradient flow in the Wasserstein space
    Ann. Inst. H. Poincare Probab. Stat. 46 (1), 1-23, (2010)

back to top