Filling Riemann surfaces by hyperbolic Schottky manifolds of negative volume

[en] 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.

Disciplines :

Mathematics

Author, co-author :

CREMASCHI, Tommaso ; University of Luxembourg > Faculty of Science, Technology and Medicine > Department of Mathematics > Team Jean-Marc SCHLENKER ; Trinity College Dublin, School of Mathematics, Ireland

GIOVANNINI, Viola ; University of Luxembourg > Faculty of Science, Technology and Medicine (FSTM) > Department of Mathematics (DMATH)

SCHLENKER, Jean-Marc ; University of Luxembourg > Faculty of Science, Technology and Medicine (FSTM) > Department of Mathematics (DMATH)

External co-authors :

yes

Language :

English

Title :

Filling Riemann surfaces by hyperbolic Schottky manifolds of negative volume

Publication date :

November 2025

Journal title :

Journal of Geometry and Physics

ISSN :

0393-0440

Publisher :

Elsevier B.V.

Volume :

217

Pages :

105628

Peer reviewed :

Peer Reviewed verified by ORBi

Additional URL :

https://api.elsevier.com/content/article/PII:S0393044025002128?httpAccept=text/xml

Funding text :

TC was partially supported by the European Union's Horizon Europe research and innovation programme under the Marie Sk\u0142odowska-Curie grant agreement No 101107744\u2013DefHyp. VG was partially supported by FNR AFR grant 15719177. JMS was partially supported by FNR OPEN grant O20/14766753. We also thank the referee for their mindful comments that helped increase the readability of the paper.

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since 12 September 2025

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