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 (8)
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
Prepublications (6)
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.
Spacetime reconstruction by order and number
arXiv:2507.01907, 16 pp.
Gromov's reconstruction theorem and measured Gromov–Hausdorff convergence in Lorentzian geometry
With Clemens Sämann
arXiv:2506.10852, 35 pp.
An elliptic proof of the splitting theorems from Lorentzian geometry
With Nicola Gigli, Robert McCann, Argam Ohanyan and Clemens Sämann
arXiv:2410.12632, 34 pp.
Exact d'Alembertian for Lorentz distance functions
arXiv:2408.16525, 84 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.
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