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arXiv · 2105.11540

Isoperimetric interpretation for the renormalized volume of convex co-compact hyperbolic 3-manifolds

Franco Vargas Pallete·Celso Viana
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Abstract

We reinterpret the renormalized volume as the asymptotic difference of the isoperimetric profiles for convex co-compact hyperbolic 3-manifolds. By similar techniques we also prove a sharp Minkowski inequality for horospherically convex sets in $\mathbb{H}^3$. Finally, we include the classification of stable constant mean curvature surfaces in regions bounded by two geodesic planes in $\mathbb{H}^3$ or in cyclic quotients of $\mathbb{H}^3$.

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Franco Vargas Pallete, Celso Viana. 2021-05-24. Isoperimetric interpretation for the renormalized volume of convex co-compact hyperbolic 3-manifolds. https://arxiv.org/abs/2105.11540

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