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

## TL;DR

This paper establishes a bound on the dual volume of the convex core of quasi-Fuchsian manifolds in terms of the Weil-Petersson distance, linking geometric and topological properties.

## Contribution

It introduces a new bound on the dual volume of convex cores using the dual Bonahon-Schläfli formula, connecting it explicitly to the Weil-Petersson distance.

## Key findings

- Dual volume is bounded by a constant times Weil-Petersson distance.
- The bound depends only on the topology of the manifold.
- Provides a quantitative link between geometric and Teichmüller theory.

## 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 $M$.