English

Filling Riemann surfaces by hyperbolic Schottky manifolds of negative volume

Differential Geometry 2025-08-18 v2 High Energy Physics - Theory Geometric Topology

Abstract

We provide conditions under which a Riemann surface XX 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 XX enough closed curves of short enough hyperbolic length.

Keywords

Cite

@article{arxiv.2405.07598,
  title  = {Filling Riemann surfaces by hyperbolic Schottky manifolds of negative volume},
  author = {Tommaso Cremaschi and Viola Giovannini and Jean-Marc Schlenker},
  journal= {arXiv preprint arXiv:2405.07598},
  year   = {2025}
}

Comments

final version accepted for publication at JGP