# The dual volume of quasi-Fuchsian manifolds and the Weil-Petersson distance

Research paper by Filippo Mazzoli

Indexed on: 11 Jul '19Published on: 10 Jul '19Published in: arXiv - Mathematics - Differential Geometry

#### Abstract

Making use of the dual Bonahon-Schl\"afli formula, we prove that the dual volume of the convex core of a quasi-Fuchsian manifold \$M\$ is bounded by an explicit constant, depending only on the topology of \$M\$, times the Weil-Petersson distance between the hyperbolic structures on the upper and lower boundary components of the convex core of \$M\$.