The dual volume of quasi-Fuchsian manifolds and the Weil-Petersson distance
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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 $M$.References
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Additional Information
- Filippo Mazzoli
- Affiliation: Department of Mathematics, University of Virginia, Charlottesville, Virginia
- MR Author ID: 1428393
- ORCID: 0000-0002-6609-915X
- Email: filippomazzoli@me.com
- Received by editor(s): September 22, 2020
- Received by editor(s) in revised form: March 9, 2021, April 18, 2021, and June 22, 2021
- Published electronically: October 8, 2021
- Additional Notes: This work was supported by the Luxembourg National Research Fund PRIDE15/10949314/GSM/Wiese
- © Copyright 2021 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 375 (2022), 695-723
- MSC (2020): Primary 30F50; Secondary 57K32, 30F40
- DOI: https://doi.org/10.1090/tran/8521
- MathSciNet review: 4358680