Upper bounds on Renormalized Volume for Schottky groups
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arXiv
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| Format: | Preprint |
| Publié: |
2019
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| _version_ | 1866912239287533568 |
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| author | Pallete, Franco Vargas |
| author_facet | Pallete, Franco Vargas |
| contents | In this article we show that for any given Riemann surface $Σ$ of genus $g$, we can bound (from above) the renormalized volume of a (hyperbolic) Schottky group with boundary at infinity conformal to $Σ$ in terms of the genus and the combined extremal lengths on $Σ$ of $(g-1)$ disjoint, non-homotopic, simple closed compressible curves. This result is used to partially answer a question posed by Maldacena about comparing renormalized volumes of Schottky and Fuchsian manifolds with the same conformal boundary. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1905_03303 |
| institution | arXiv |
| publishDate | 2019 |
| record_format | arxiv |
| spellingShingle | Upper bounds on Renormalized Volume for Schottky groups Pallete, Franco Vargas Differential Geometry Geometric Topology In this article we show that for any given Riemann surface $Σ$ of genus $g$, we can bound (from above) the renormalized volume of a (hyperbolic) Schottky group with boundary at infinity conformal to $Σ$ in terms of the genus and the combined extremal lengths on $Σ$ of $(g-1)$ disjoint, non-homotopic, simple closed compressible curves. This result is used to partially answer a question posed by Maldacena about comparing renormalized volumes of Schottky and Fuchsian manifolds with the same conformal boundary. |
| title | Upper bounds on Renormalized Volume for Schottky groups |
| topic | Differential Geometry Geometric Topology |
| url | https://arxiv.org/abs/1905.03303 |