8 citations · 13 across the 11 of their papers we have counts for
11 papers
The radial part of -Brownian motion
Mathias Braun
We initiate a geometric theory of -Brownian motion, the nonlinear Markov process associated with the -Laplacian introduced by Barbu-Rehmeier-Röckner. More precisely, we analy…
Comparison theory for Lipschitz spacetimes
Mathias Braun, Marta Sálamo Candal
We prove a globally hyperbolic spacetime with locally Lipschitz continuous metric and timelike distributional Ricci curvature bounded from below obeys the timelike measure contract…
Optimal transport and timelike lower Ricci curvature bounds on Finsler spacetimes
Mathias Braun, Shin-ichi Ohta
We prove that a Finsler spacetime endowed with a smooth reference measure whose induced weighted Ricci curvature is bounded from below by a real number …
Timelike Ricci bounds for low regularity spacetimes by optimal transport
Mathias Braun, Matteo Calisti
We prove that a globally hyperbolic smooth spacetime endowed with a -Lorentzian metric whose Ricci tensor is bounded from below in all timelike directions, in…
Rényi's entropy on Lorentzian spaces. Timelike curvature-dimension conditions
Mathias Braun
For a Lorentzian space measured by in the sense of Kunzinger, Sämann, Cavalletti, and Mondino, we introduce and study synthetic notions of timelike lower Ricci curva…
Good geodesics satisfying the timelike curvature-dimension condition
Mathias Braun
Let be a causally closed, -globally hyperbolic, regular measured Lorentzian geodesic space satisfying the weak timelike curvat…
Heat kernel bounds and Ricci curvature for Lipschitz manifolds
Mathias Braun, Chiara Rigoni
Given any -dimensional Lipschitz Riemannian manifold with heat kernel , we establish uniform upper bounds on which can always be decoupled in sp…
Vector calculus for tamed Dirichlet spaces
Mathias Braun
In the language of -modules proposed by Gigli, we introduce a first order calculus on a topological Lusin measure space carrying a quasi-regular, stron…
Heat flow on 1-forms under lower Ricci bounds. Functional inequalities, spectral theory, and heat kernel
Mathias Braun
We study the canonical heat flow on the cotangent module over an space , $K\in\boldsymb…
Heat flow regularity, Bismut-Elworthy-Li's derivative formula, and pathwise couplings on Riemannian manifolds with Kato bounded Ricci curvature
Mathias Braun, Batu Güneysu
We prove that if the Ricci tensor of a geodesically complete Riemannian manifold , endowed with the Riemannian distance and the Riemannian measure $\…
Optimal transport, gradient estimates, and pathwise Brownian coupling on spaces with variable Ricci bounds
Mathias Braun, Karen Habermann, Karl-Theodor Sturm
Given a metric measure space and a lower semicontinuous, lower bounded function , we prove the equivalence of the synthetic ap…