Asymptotic behavior of Cauchy hypersurfaces in constant curvature space-times
| hal.structure.identifier | Institut de Mathématiques de Bordeaux [IMB] | |
| dc.contributor.author | BELRAOUTI, Mehdi | |
| dc.date.accessioned | 2024-04-04T03:18:44Z | |
| dc.date.available | 2024-04-04T03:18:44Z | |
| dc.identifier.uri | https://oskar-bordeaux.fr/handle/20.500.12278/194441 | |
| dc.description.abstractEn | We study the asymptotic behavior of convex Cauchy hypersurfaces on maximal globally hyperbolic spatially compact space-times of constant curvature. We generalise the result of [11] to the (2+1) de Sitter and anti de Sitter cases. We prove that in these cases the level sets of quasi-concave times converge in the Gromov equivariant topology, when time goes to 0, to a real tree. Moreover, this limit does not depend on the choice of the time function. We also consider the problem of asymptotic behavior in the flat (n+1) dimensional case. We prove that the level sets of quasi-concave times converge in the Gromov equivariant topology, when time goes to 0, to a CAT (0) metric space. Moreover, this limit does not depend on the choice of the time function. | |
| dc.language.iso | en | |
| dc.title.en | Asymptotic behavior of Cauchy hypersurfaces in constant curvature space-times | |
| dc.type | Document de travail - Pré-publication | |
| dc.subject.hal | Mathématiques [math]/Géométrie différentielle [math.DG] | |
| dc.identifier.arxiv | 1503.06343 | |
| bordeaux.hal.laboratories | Institut de Mathématiques de Bordeaux (IMB) - UMR 5251 | * |
| bordeaux.institution | Université de Bordeaux | |
| bordeaux.institution | Bordeaux INP | |
| bordeaux.institution | CNRS | |
| hal.identifier | hal-01134068 | |
| hal.version | 1 | |
| hal.origin.link | https://hal.archives-ouvertes.fr//hal-01134068v1 | |
| bordeaux.COinS | ctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.au=BELRAOUTI,%20Mehdi&rft.genre=preprint |
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