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Upper bounds on Renormalized Volume for Schottky groups

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 نشر من قبل Franco Vargas Pallete
 تاريخ النشر 2019
  مجال البحث
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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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