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arXiv · 2412.08967

Low regularity approach to Bartnik's conjecture

José Luis Flores·Jónatan Herrera·Didier A. Solis
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Abstract

In this work we establish a version of the Bartnik Splitting Conjecture in the context of Lorentzian length spaces. In precise terms, we show that under an appropriate timelike completeness condition, a globally hyperbolic Lorentzian length space of the form $\Sigma\times \mathbb{R}$ with $\Sigma$ compact splits as a metric Lorentzian product, provided it has non negative timelike curvature bounds. This is achieved by showing that the causal boundary of that Lorentzian length space consists on a single point.

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BibTeXRIS

José Luis Flores, Jónatan Herrera, Didier A. Solis. 2024-12-12. Low regularity approach to Bartnik's conjecture. https://arxiv.org/abs/2412.08967

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