7 papers
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…
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…
A Toponogov globalisation result for Lorentzian length spaces
Tobias Beran, John Harvey, Lewis Napper +1
In the synthetic geometric setting introduced by Kunzinger and Sämann, we present an analogue of Toponogov's Globalisation Theorem which applies to Lorentzian length spaces with l…
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…