Filling Riemann surfaces by hyperbolic Schottky manifolds of negative volume

2024/05/13 by Tommaso Cremaschi, Cremaschi, Tommaso, Viola Giovannini +3 · 2 citations
Mathematics · #Geometric and Algebraic Topology #Geometric Analysis and Curvature Flows #Mathematical Dynamics and Fractals

paper · pdf · doi:10.48550/arxiv.2405.07598

Abstract

We provide conditions under which a Riemann surface X is the asymptotic boundary of a convex co-compact hyperbolic manifold, homeomorphic to a handlebody, of negative renormalized volume. We prove that this is the case when there are on X enough closed curves of short enough hyperbolic length.

Cited by

• Volume functions and boundary data of 3-dimensional hyperbolic manifolds
• Adapted Renormalized Volume for Hyperbolic 3-Manifolds with Compressible Boundary

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