10 papers
Curvature bounds, regularity and inextendibility of spacetimes
Tobias Beran, John Harvey, Clemens Sämann
We provide a completely new relation between curvature bounds and definiteness of the causal character of maximizers by exploiting the robust notion of synthetic curvature. This en…
Reshetnyak Majorisation and discrete upper curvature bounds for Lorentzian length spaces
Tobias Beran, Felix Rott
We present an analogue to the Majorisation Theorem of Reshetnyak in the setting of Lorentzian length spaces with upper curvature bounds: given two future-directed timelike rectifia…
Concavity of spacetimes
Tobias Beran, Darius Erös, Shin-ichi Ohta +1
Motivated by recent breathtaking progress in the synthetic study of Lorentzian geometry, we investigate the local concavity of time separation functions on Finsler spacetimes as a…
Hyperbolic angles in Lorentzian length spaces and timelike curvature bounds
Tobias Beran, Clemens Sämann
Within the synthetic-geometric framework of Lorentzian (pre-)length spaces developed in Kunzinger and Sämann (Ann. Glob. Anal. Geom. 54(3):399--447, 2018) we introduce a notion of…
A Splitting Theorem for non-positively curved Lorentzian spaces
Joe Barton, Tobias Beran, Mauricio Che +3
We prove a splitting theorem for Lorentzian pre-length spaces with global non-positive timelike curvature. Additionally, we extend the first variation formula to spaces with any ti…
Alexandrov's Patchwork and the Bonnet--Myers Theorem for Lorentzian length spaces
Tobias Beran, Lewis Napper, Felix Rott
We present several key results for Lorentzian pre-length spaces with global timelike curvature bounds. Most significantly, we construct a Lorentzian analogue to Alexandrov's Patchw…