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Register a new userIsoperimetric interpretation for the renormalized volume of convex co-compact hyperbolic 3-manifolds
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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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