1 citations · 1 across the 8 of their papers we have counts for
10 papers
Causal Sobolev spaces and gradient flows
Mathias Braun, Nicola Gigli, Robert McCann +1
We develop a relaxation-based approach to Sobolev functions and Cheeger energies on metric spacetimes, in analogy with the construction used in positive signature. For an exponent…
A synthetic Gannon-Lee incompleteness theorem
Mathias Braun, Carlo Rotolo
We prove the Gannon-Lee incompleteness theorem for globally hyperbolic spacetimes. We assume the synthetic null energy condition of Ketterer and a trappedness condition we call "sy…
A Lorentzian splitting theorem for continuously differentiable metrics and weights
Mathias Braun, Nicola Gigli, Robert J. McCann +2
We prove a splitting theorem for globally hyperbolic, weighted spacetimes with metrics and weights of regularity by combining elliptic techniques for the negative homogeneity…
Spacetime reconstruction by order and number
Mathias Braun
We show that the random adjacency matrices induced by the chronological relations and i.i.d. samples of two spacetimes coincide in law if and only if the spacetimes in question are…
Gromov's reconstruction theorem and measured Gromov-Hausdorff convergence in Lorentzian geometry
Mathias Braun, Clemens Sämann
We establish Gromov's celebrated reconstruction theorem in Lorentzian geometry. Alongside this result, we introduce and study a natural concept of isomorphy of normalized bounded L…
New perspectives on the d'Alembertian from general relativity. An invitation
Mathias Braun
This survey has multiple objectives. First, we motivate and review a new distributional notion of the d'Alembertian from mathematical relativity, more precisely, a nonlinear -ve…
An elliptic proof of the splitting theorems from Lorentzian geometry
Mathias Braun, Nicola Gigli, Robert J. McCann +2
We provide a new proof of the splitting theorems from Lorentzian geometry, in which simplicity is gained by sacrificing linearity of the d'Alembertian to recover ellipticity. We ex…
Exact d'Alembertian for Lorentz distance functions
Mathias Braun
We refine a recent distributional notion of d'Alembertian of a signed Lorentz distance function to an achronal set in a metric measure spacetime obeying the timelike measure contra…
A nonlinear d'Alembert comparison theorem and causal differential calculus on metric measure spacetimes
Tobias Beran, Mathias Braun, Matteo Calisti +5
We introduce a variational first-order Sobolev calculus on metric measure spacetimes. The key object is the maximal weak subslope of an arbitrary causal function, which plays the r…
Causal convergence conditions through variable timelike Ricci curvature bounds
Mathias Braun, Robert J. McCann
We describe a nonsmooth notion of globally hyperbolic, regular length metric spacetimes . It is based on ideas of Kunzinger-Sämann, but does not require Lipschitz c…