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| Format: | Preprint |
| Veröffentlicht: |
2026
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| Online-Zugang: | https://arxiv.org/abs/2603.09598 |
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| _version_ | 1866918381391708160 |
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| author | Labourie, François Toulisse, Jérémy Wang, Yilin |
| author_facet | Labourie, François Toulisse, Jérémy Wang, Yilin |
| contents | We investigate and define in this paper, in the context of the correspondence between anti-de Sitter $3$-space and $(1,1)$-conformal metrics, the analogs of $\cW$-volume, Epstein surfaces, and Liouville action. These notions were well-studied in the correspondence between $3d$-hyperbolic manifolds and $2d$ conformal metrics. We apply our construction to positive curves in flag manifolds equipped with a positive structure to obtain invariants of these curves that are finite in the case of piecewise circles. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_09598 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Lorentz--Epstein surfaces and a Liouville action for positive curves Labourie, François Toulisse, Jérémy Wang, Yilin Differential Geometry We investigate and define in this paper, in the context of the correspondence between anti-de Sitter $3$-space and $(1,1)$-conformal metrics, the analogs of $\cW$-volume, Epstein surfaces, and Liouville action. These notions were well-studied in the correspondence between $3d$-hyperbolic manifolds and $2d$ conformal metrics. We apply our construction to positive curves in flag manifolds equipped with a positive structure to obtain invariants of these curves that are finite in the case of piecewise circles. |
| title | Lorentz--Epstein surfaces and a Liouville action for positive curves |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/2603.09598 |