Flexible hyperbolic cone metrics on the genus 2 surface

A negatively curved hyperbolic cone metric on a surface is rigid if it is determined by the support of its Liouville current. We use a theorem of Erlandsson, Leininger, and Sadanand to show that there are nine mapping class group orbits of equivalence classes of non-rigid (aka flexible) metrics in the case of the genus 2 surface.

Publication Details

Journal
ArXiv.org
Published
2025-07-25
Primary Topic
Geometric and Algebraic Topology
Type
article
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article

Flexible hyperbolic cone metrics on the genus 2 surface

ArXiv.org
Geometric and Algebraic Topology
article

Flexible hyperbolic cone metrics on the genus 2 surface

article en

Abstract

A negatively curved hyperbolic cone metric on a surface is rigid if it is determined by the support of its Liouville current. We use a theorem of Erlandsson, Leininger, and Sadanand to show that there are nine mapping class group orbits of equivalence classes of non-rigid (aka flexible) metrics in the case of the genus 2 surface.

ArXiv.org
Openalex Percentile: Top 41%
Geometric and Algebraic Topology
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Flexible hyperbolic cone metrics on the genus 2 surface · ArXiv.org (2025) | TGRS Research Map | TGRS