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

@article{Mazzoli2019TheDV, title={The dual volume of quasi-Fuchsian manifolds and the Weil-Petersson distance}, author={Filippo Mazzoli}, journal={arXiv: Differential Geometry}, year={2019} }

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

## 5 Citations

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Given a differentiable deformation of geometrically finite hyperbolic $3$-manifolds $(M_t)_t$, the Bonahon-Schlafli formula expresses the derivative of the volume of the convex cores $(C M_t)_t$ in…

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Given a differentiable deformation of geometrically finite hyperbolic 3-manifolds (Mt)t , the Bonahon-Schläfli formula [Bon98a] expresses the derivative of the volume of the convex cores (CMt)t in…

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