Beran, Tobias, Harvey, John  ORCID: https://orcid.org/0000-0001-9211-0060, Napper, Lewis and Rott, Felix
2025.
A Toponogov globalisation result for Lorentzian length spaces.
Mathematische Annalen
10.1007/s00208-025-03167-w
|
Preview |
PDF
- Published Version
Available under License Creative Commons Attribution. Download (711kB) | Preview |
Abstract
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 lower (timelike) curvature bounds. Our approach utilises a “cat’s cradle” construction akin to that which appears in several proofs in the metric setting. On the road to our main result, we also provide a lemma regarding the subdivision of triangles in spaces with a local lower curvature bound and a synthetic Lorentzian version of the Lebesgue Number Lemma. Several properties of time functions and the null distance on globally hyperbolic Lorentzian length spaces are also highlighted. We conclude by presenting several applications of our results, including versions of the Bonnet–Myers Theorem and the Splitting Theorem for Lorentzian length spaces with local lower curvature bounds, as well as discussion of stability of curvature bounds under Gromov–Hausdorff convergence.
| Item Type: | Article |
|---|---|
| Date Type: | Published Online |
| Status: | In Press |
| Schools: | Schools > Mathematics |
| Publisher: | Springer |
| ISSN: | 0025-5831 |
| Date of First Compliant Deposit: | 2 April 2025 |
| Date of Acceptance: | 29 March 2025 |
| Last Modified: | 20 May 2025 12:25 |
| URI: | https://orca.cardiff.ac.uk/id/eprint/177347 |
Actions (repository staff only)
 |
Edit Item |
Altmetric
Altmetric