45 citations · 76 across the 11 of their papers we have counts for
11 papers
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…
A brief introduction to non-regular spacetime geometry
Clemens Sämann
We give a brief non-technical introduction to non-regular spacetime geometry. In particular, we discuss how curvature, and hence gravity, can be defined without a smooth (different…
Cut-and-paste for impulsive gravitational waves with : The geometric picture
Jiri Podolsky, Clemens Sämann, Roland Steinbauer +1
Impulsive gravitational waves in Minkowski space were introduced by Roger Penrose at the end of the 1960s, and have been widely studied over the decades. Here we focus on non-expan…
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…
The global existence, uniqueness and C^1-regularity of geodesics in nonexpanding impulsive gravitational waves
Jiri Podolsky, Clemens Sämann, Roland Steinbauer +1
We study geodesics in the complete family of nonexpanding impulsive gravitational waves propagating in spaces of constant curvature, that is Minkowski, de Sitter and anti-de Sitter…
The globally hyperbolic metric splitting for non-smooth wave-type space-times
Günther Hörmann, Clemens Sämann
We investigate a generalization of the so-called metric splitting of globally hyperbolic space-times to non-smooth Lorentzian manifolds and show the existence of this metric splitt…