24 citations · 42 across the 12 of their papers we have counts for
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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…