28 citations · 172 across the 17 of their papers we have counts for
7 papers · 1 filter
Doubling for chronological diamonds in Lorentzian geometry
Mauricio Che, Sebastian Gieger, Clemens Sämann
We define doubling conditions for measured Lorentzian length spaces in terms of chronological diamonds, and prove that such conditions are implied by suitable timelike curvature bo…
An elliptic proof of the splitting theorems from Lorentzian geometry
Mathias Braun, Nicola Gigli, Robert J. McCann +2
We provide a new proof of the splitting theorems from Lorentzian geometry, in which simplicity is gained by sacrificing linearity of the d'Alembertian to recover ellipticity. We ex…
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…
Lorentz meets Lipschitz
Christian Lange, Alexander Lytchak, Clemens Sämann
We show that maximal causal curves for a Lipschitz continuous Lorentzian metric admit a -parametrization and that they solve the geodesic equation in the sense o…
The future is not always open
James D. E. Grant, Michael Kunzinger, Clemens Sämann +1
We demonstrate the breakdown of several fundamentals of Lorentzian causality theory in low regularity. Most notably, chronological futures (defined naturally using locally Lipschit…
Lorentzian length spaces
Michael Kunzinger, Clemens Sämann
We introduce an analogue of the theory of length spaces into the setting of Lorentzian geometry and causality theory. The rôle of the metric is taken over by the time separation fu…
Geodesic completeness of generalized space-times
Clemens Sämann, Roland Steinbauer
We define the notion of geodesic completeness for semi-Riemannian metrics of low regularity in the framework of the geometric theory of generalized functions. We then show complete…