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

Filippo Mazzoli

Geometry & Topology 27 (2023) 2319–2346
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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