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arXiv · 1905.03303

Upper bounds on Renormalized Volume for Schottky groups

Franco Vargas Pallete
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Abstract

In this article we show that for any given Riemann surface $\Sigma$ of genus $g$, we can bound (from above) the renormalized volume of a (hyperbolic) Schottky group with boundary at infinity conformal to $\Sigma$ in terms of the genus and the combined extremal lengths on $\Sigma$ 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.

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BibTeXRIS

Franco Vargas Pallete. 2019-05-08. Upper bounds on Renormalized Volume for Schottky groups. https://arxiv.org/abs/1905.03303

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