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arXiv · 2609.03723

Continuity of the renormalised volume between Epstein surfaces with respect to the Weil--Petersson topology

Dorian Martino
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Abstract

We prove that the renormalised volume between the two Epstein surfaces generated by a Weil--Petersson quasicircle is continuous with respect to the Weil--Petersson topology. As a consequence, we prove that the universal Liouville action is proportional to this renormalised volume for any Weil--Petersson quasicircle.

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Dorian Martino. 2026-09-03. Continuity of the renormalised volume between Epstein surfaces with respect to the Weil--Petersson topology. https://arxiv.org/abs/2609.03723

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