A Toponogov globalisation result for Lorentzian length spaces
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Summary
This summary is machine-generated.This study introduces a new Globalisation Theorem for Lorentzian length spaces with timelike curvature bounds, utilizing a novel "cat
Area Of Science
- Differential Geometry
- General Relativity
- Metric Geometry
Background
- Lorentzian length spaces are a generalization of Lorentzian manifolds.
- Curvature bounds are crucial for understanding the geometry of these spaces.
- Toponogov's Globalisation Theorem is a fundamental result in Riemannian geometry.
Purpose Of The Study
- To present a synthetic analogue of Toponogov's Globalisation Theorem for Lorentzian length spaces.
- To extend results concerning curvature bounds in Lorentzian geometry.
- To explore applications in general relativity and geometric analysis.
Main Methods
- Utilizing a
- Meta_Description='Explore a new Globalisation Theorem for Lorentzian length spaces with timelike curvature bounds, with applications in geometry and relativity.'
Main Results
- A synthetic analogue of Toponogov's Globalisation Theorem for Lorentzian length spaces with lower timelike curvature bounds.
- A lemma on triangle subdivision and a synthetic Lorentzian Lebesgue Number Lemma.
- Properties of time functions and null distance on globally hyperbolic Lorentzian length spaces.
Conclusions
- The presented results extend classical geometric theorems to the synthetic Lorentzian setting.
- Applications include versions of the Bonnet-Myers and Splitting Theorems.
- Stability of curvature bounds under Gromov-Hausdorff convergence is discussed.
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