# The infimum of the dual volume of convex co-compact hyperbolic $3$-manifolds

@inproceedings{Mazzoli2021TheIO, title={The infimum of the dual volume of convex co-compact hyperbolic \$3\$-manifolds}, author={Filippo Mazzoli}, year={2021} }

We show that the infimum of the dual volume of the convex core of a convex co-compact 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 quasi-Fuchsian manifold in terms of the length of its bending measured lamination, with optimal multiplicative constant.

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