arXiv subjects

Sebastian Gieger

Publications and source records attributed to Sebastian Gieger.

3 recordsLinked to original sources

arXiv2026

Doubling for chronological diamonds in Lorentzian geometry

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 bounds. In particular, for the first time, we relate doubling to curvature bounds in Lorentzian geometry. As a consequence, we obtain compactness results for Lorentzian generalized cones with respect to the Lorentzian Gromov--Hausdorff convergence introduced by Mondino--S\"amann.

math.DG↗

arXiv2026

A Splitting Theorem for non-positively curved Lorentzian spaces

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 timelike curvature bound, either from above or below, and different from 0.

math.DG↗

arXiv2025

A synthetic Lorentzian Cartan-Hadamard theorem

We formulate and prove a synthetic Lorentzian Cartan-Hadamard theorem. This result both transfers the corresponding statement for locally convex metric spaces established by S. Alexander and R. Bishop to the Lorentzian setting, and simultaneously generalizes the smooth Lorentzian theorem discussed by J. Beem and P. Ehrlich to the recently established framework of synthetic Lorentzian geometry. Our approach is based on an appropriate notion of local concavity for Lorentzian (pre-)length spaces, which allows us to establish existence and uniqueness of timelike geodesics between any pair of timelike related points under the additional assumptions of global hyperbolicity and future one-connectedness. We also provide a globalization result for our notion of concavity in the setting of Lorentzian length spaces, and apply our results to obtain a globalization statement for nonnegative upper timelike curvature bounds.

math.MG↗