Convex surfaces with prescribed induced metrics in anti-de Sitter spacetimes
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866916234004529152 |
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| author | Chen, Qiyu Schlenker, Jean-Marc |
| author_facet | Chen, Qiyu Schlenker, Jean-Marc |
| contents | Let $S$ be a closed surface of genus at least $2$, let $h$ be a smooth metric of curvature $K<-1$ on $S$, and let $h_0$ be a hyperbolic metric on $S$. We show that there exists a unique quasifuchsian AdS spacetime with left metric isotopic to $h_0$, containing a past-convex Cauchy surface with induced metric isotopic to $h$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_01912 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Convex surfaces with prescribed induced metrics in anti-de Sitter spacetimes Chen, Qiyu Schlenker, Jean-Marc Differential Geometry Geometric Topology Let $S$ be a closed surface of genus at least $2$, let $h$ be a smooth metric of curvature $K<-1$ on $S$, and let $h_0$ be a hyperbolic metric on $S$. We show that there exists a unique quasifuchsian AdS spacetime with left metric isotopic to $h_0$, containing a past-convex Cauchy surface with induced metric isotopic to $h$. |
| title | Convex surfaces with prescribed induced metrics in anti-de Sitter spacetimes |
| topic | Differential Geometry Geometric Topology |
| url | https://arxiv.org/abs/2405.01912 |