A sharp isoperimetric-type inequality for Lorentzian spaces satisfying timelike Ricci lower bounds
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866915133579591680 |
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| author | Cavalletti, Fabio Mondino, Andrea |
| author_facet | Cavalletti, Fabio Mondino, Andrea |
| contents | The paper establishes a sharp and rigid isoperimetric-type inequality in Lorentzian signature under the assumption of Ricci curvature bounded below in the timelike directions. The inequality is proved in the high generality of Lorentzian pre-length spaces satisfying timelike Ricci lower bounds in a synthetic sense via optimal transport, the so-called $\mathsf{TCD}^e_p(K,N)$ spaces. The results are new already for smooth Lorentzian manifolds. Applications include an upper bound on the area of achronal hypersurfaces inside the interior of a black hole (original already in Schwarzschild) and an upper bound on the area of achronal hypersurfaces in cosmological spacetimes. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_03949 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A sharp isoperimetric-type inequality for Lorentzian spaces satisfying timelike Ricci lower bounds Cavalletti, Fabio Mondino, Andrea Metric Geometry Mathematical Physics Differential Geometry The paper establishes a sharp and rigid isoperimetric-type inequality in Lorentzian signature under the assumption of Ricci curvature bounded below in the timelike directions. The inequality is proved in the high generality of Lorentzian pre-length spaces satisfying timelike Ricci lower bounds in a synthetic sense via optimal transport, the so-called $\mathsf{TCD}^e_p(K,N)$ spaces. The results are new already for smooth Lorentzian manifolds. Applications include an upper bound on the area of achronal hypersurfaces inside the interior of a black hole (original already in Schwarzschild) and an upper bound on the area of achronal hypersurfaces in cosmological spacetimes. |
| title | A sharp isoperimetric-type inequality for Lorentzian spaces satisfying timelike Ricci lower bounds |
| topic | Metric Geometry Mathematical Physics Differential Geometry |
| url | https://arxiv.org/abs/2401.03949 |