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

Abstract

Making use of the dual Bonahon-Schläfli 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 $M$.

Expanded proof of former Proposition 4.3 (now 4.4), added Lemma 4.3

References in corpus (2)

• Notes on the Schwarzian tensor and measured foliations at infinity of quasifuchsian manifolds
• The dual Bonahon-Schläfli formula

Cited by in corpus (2)

• Constant Gaussian curvature foliations and Schläfli formulas of hyperbolic $3$-manifolds
• The infimum of the dual volume of convex co-compact hyperbolic $3$-manifolds