Convexity of the renormalized volume of hyperbolic $3$-manifolds

Sergiu Moroianu

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arXiv · 1503.07981

Convexity of the renormalized volume of hyperbolic $3$-manifolds

Sergiu Moroianu

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Abstract

The Hessian of the renormalized volume of geometrically finite hyperbolic $3$-manifolds without rank-$1$ cusps, computed at the hyperbolic metric $g$ with totally geodesic boundary of the convex core, is shown to be a strictly positive bilinear form on the tangent space to Teichmüller space. The metric $g$ is known from results of Bonahon and Storm to be an absolute minimum for the volume of the convex core. We deduce the strict convexity of the functional volume of the convex core at its minimum point.

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BibTeX RIS

Sergiu Moroianu. 2015-03-27. Convexity of the renormalized volume of hyperbolic $3$-manifolds. https://arxiv.org/abs/1503.07981

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