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Mathias Braun
  • Home
  • Research
  • Publications
  • Activities
  • Teaching
  • Vitae
  • Contact
  • More
    • Home
    • Research
    • Publications
    • Activities
    • Teaching
    • Vitae
    • Contact

Preprints (6)

  • The radial part of p-Brownian motion
    arXiv:2609.11558, 31 pp.

  • Comparison theory for Lipschitz spacetimes
    With Marta Sálamo Candal
    arXiv:2603.24195, 52 pp.

  • A synthetic Gannon–Lee incompleteness theorem
    With Carlo Rotolo
    arXiv:2602.14246, 20 pp.

  • A Lorentzian splitting theorem for continuously differentiable metrics and weights
    With Nicola Gigli, Robert McCann, Argam Ohanyan and Clemens Sämann
    arXiv:2507.06836, 44 pp.

  • Gromov's reconstruction theorem and measured Gromov–Hausdorff convergence in Lorentzian geometry
    With Clemens Sämann
    arXiv:2506.10852, 35 pp.

  • A nonlinear d'Alembert comparison theorem and causal differential calculus on metric measure spacetimes
    With Tobias Beran, Matteo Calisti, Nicola Gigli, Robert McCann, Argam Ohanyan, Felix Rott and Clemens Sämann
    arXiv:2408.15968, 112 pp.

Monographs (2)

  • Vector calculus for tamed Dirichlet spaces
    Memoirs of the American Mathematical Society 303 (2024), no. 1522, 118 pp.

  • Causal convergence conditions through variable timelike Ricci curvature bounds
    With Robert McCann
    Memoirs of the European Mathematical Society, in press, 109 pp.

Publications (11)

  • Exact d'Alembertian for Lorentz distance functions
    Calculus of Variations and Partial Differential Equations, to appear, 84 pp.

  • An elliptic proof of the splitting theorems from Lorentzian geometry
    With Nicola Gigli, Robert McCann, Argam Ohanyan and Clemens Sämann
    Communications of the American Mathematical Society, to appear, 34 pp.

  • Spacetime reconstruction by order and number
    Classical and Quantum Gravity, 43 (2026), no. 4, Paper No. 045015, 15 pp.

  • Optimal transport and timelike lower Ricci curvature bounds on Finsler spacetimes
    With Shin-ichi Ohta
    Transactions of the American Mathematical Society 377 (2024), no. 5, 3529–3576

  • Heat kernel bounds and Ricci curvature for Lipschitz manifolds
    With Chiara Rigoni
    Stochastic Processes and their Applications 170 (2024), Paper No. 104292, 21 pp.

  • Timelike Ricci bounds for low regularity spacetimes by optimal transport
    With Matteo Calisti
    Communications in Contemporary Mathematics 26 (2024), no. 9, Paper No. 2350049, 23 pp.

  • Rényi's entropy on Lorentzian spaces. Timelike curvature-dimension conditions
    Journal de Mathématiques Pures et Appliquées (9) 177 (2023), 46–128

  • Good geodesics satisfying the timelike curvature-dimension condition
    Nonlinear Analysis 229 (2023), Paper No. 113205, 30 pp.

  • Heat flow on 1-forms under lower Ricci bounds. Functional inequalities, spectral theory, and heat kernel
    Journal of Functional Analysis 283 (2022), no. 7, Paper No. 109599, 65 pp.

  • Heat flow regularity, Bismut–Elworthy–Li's derivative formula, and pathwise couplings on Riemannian manifolds with Kato bounded Ricci curvature
    With Batu Güneysu
    Electronic Journal of Probability 26 (2021), Paper No. 129, 1–25

  • Optimal transport, gradient estimates, and pathwise Brownian coupling on spaces with variable Ricci bounds
    With Karen Habermann and Karl-Theodor Sturm
    Journal de Mathématiques Pures et Appliquées 147 (2021), 60–97

Proceedings (2)

  • New perspectives on the d’Alembertian from general relativity. An invitation
    Indagationes Mathematicae, in press, 49 pp.

  • Vector calculus for tamed Dirichlet spaces
    Oberwolfach Reports 58 (2021), 27–30

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