The infimum of the dual volume of convex cocompact hyperbolic $3$manifolds
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 quasiisometric deformations. We deduce a linear lower bound of the volume of the convex core of a quasiFuchsian manifold in terms of the length of its bending measured lamination, with optimal multiplicative constant.
 Publication:

arXiv eprints
 Pub Date:
 January 2021
 arXiv:
 arXiv:2101.09380
 Bibcode:
 2021arXiv210109380M
 Keywords:

 Mathematics  Differential Geometry;
 Mathematics  Geometric Topology;
 30F40 (Primary) 57M50;
 52A15
 EPrint:
 Updated introduction. To appear in Geometry &