Flexible hyperbolic cone metrics on the genus 2 surface

2025/07/25 by Chui, Katherine, Russell, Jacob
#57K20 #57M50 #FOS: Mathematics #Geometric Topology (math.GT)

paper · doi:10.48550/arxiv.2507.19677

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.

Citations

• Hyperbolic cone metrics and billiards
• You can hear the shape of a billiard table: Symbolic dynamics and rigidity for flat surfaces
• Marked length spectrum rigidity in nonpositive curvature with\n singularities
• Length spectral rigidity of non-positively curved surfaces

Related

• Hyperbolic cone metrics and billiards
• Rigidity for Nonnegatively Curved Metrics on S²xR³
• Marked length spectral rigidity for flat metrics
• Changing topological type of compression bodies through cone manifolds
• On finite marked length spectral rigidity of hyperbolic cone surfaces and the Thurston metric