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

Mazzoli, Filippo

doi:10.2140/gt.2023.27.2319

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

Filippo Mazzoli

Geometry & Topology 27 (2023) 2319–2346

DOI: 10.2140/gt.2023.27.2319

Abstract

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.

Keywords

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

Mathematical Subject Classification

Primary: 30F40

Secondary: 52A15, 57M50

References

Publication

Received: 1 March 2021

Revised: 23 December 2021

Accepted: 24 January 2022

Published: 25 August 2023

Proposed: Ian Agol

Seconded: Mladen Bestvina, David Fisher

Authors

Filippo Mazzoli
Department of Mathematics University of Virginia Charlotteville, VA United States

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Volume 27, issue 6 (2023)