45 citations · 76 across the 11 of their papers we have counts for
7 papers · 1 filter
Conformal transformations of metric spaces and Lorentzian pre-length spaces
Miguel Manzano, Karim Mosani, Clemens Sämann +1
We introduce conformal transformations in the synthetic setting of metric spaces and Lorentzian (pre-)length spaces. Our main focus lies on the Lorentzian case, where, motivated by…
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…
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…
Generalized cones admitting a curvature-dimension condition
Matteo Calisti, Christian Ketterer, Clemens Sämann
We study (generalized) cones over metric spaces, both in Riemannian and Lorentzian signature. In particular, we establish synthetic lower Ricci curvature bounds à la Lott-Villani-S…
Lorentzian Gromov-Hausdorff convergence and pre-compactness
Andrea Mondino, Clemens Sämann
The goal of the paper is to introduce a convergence à la Gromov-Hausdorff for Lorentzian spaces, building on -nets consisting of causal diamonds and relying only on the time sep…
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…
Global hyperbolicity for spacetimes with continuous metrics
Clemens Sämann
We show that the definition of global hyperbolicity in terms of the compactness of the causal diamonds and non-total imprisonment can be extended to spacetimes with continuous metr…