24 citations · 55 across the 14 of their papers we have counts for
14 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…
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…
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…
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…
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…
The equivalence of smooth and synthetic notions of timelike sectional curvature bounds
Tobias Beran, Michael Kunzinger, Argam Ohanyan +1
Timelike sectional curvature bounds play an important role in spacetime geometry, both for the understanding of classical smooth spacetimes and for the study of Lorentzian (pre-)le…
Bonnet-Myers rigidity theorem for globally hyperbolic Lorentzian length spaces
Tobias Beran
We prove a synthetic Bonnet-Myers rigidity theorem for globally hyperbolic Lorentzian length spaces with global curvature bounded below by and an open distance realizer of le…
Characterizing intrinsic Lorentzian length spaces via -midpoints
Tobias Beran, Felix Rott
In metric geometry, the question of whether a distance metric is given by the length of curves can be decided via the existence of midpoints with respect to the metric . We adap…
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 lo…
On curvature bounds in Lorentzian length spaces
Tobias Beran, Michael Kunzinger, Felix Rott
We introduce several new notions of (sectional) curvature bounds for Lorentzian pre-length spaces: On the one hand, we provide convexity/concavity conditions for the (modified) tim…
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…
The splitting theorem for globally hyperbolic Lorentzian length spaces with non-negative timelike curvature
Tobias Beran, Argam Ohanyan, Felix Rott +1
In this work, we prove a synthetic splitting theorem for globally hyperbolic Lorentzian length spaces with global non-negative timelike curvature containing a complete timelike lin…
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…
Gluing constructions for Lorentzian length spaces
Tobias Beran, Felix Rott
We introduce an analogue to the amalgamation of metric spaces into the setting of Lorentzian pre-length spaces. This provides a very general process of constructing new spaces out…