The infimum of the dual volume of convex cocompact hyperbolic 3–manifolds

Mazzoli, Filippo¹

¹ Department of Mathematics, University of Virginia, Charlotteville, VA, United States

Geometry & topology, Tome 27 (2023) no. 6, pp. 2319-2346.

Résumé

We show that the infimum of the dual volume of the convex core of a convex cocompact hyperbolic $3$–manifold with incompressible boundary coincides with the infimum of the Riemannian volume of its convex core, as we vary the geometry by quasi-isometric deformations. We deduce a linear lower bound of the volume of the convex core of a quasi-Fuchsian manifold in terms of the length of its bending measured lamination, with optimal multiplicative constant.

Détail

DOI : 10.2140/gt.2023.27.2319

Keywords: hyperbolic geometry, dual volume, Kleinian groups, convex core, convex cocompact

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