Minimal diffeomorphism between hyperbolic surfaces with cone singularities

Jérémy Toulisse

paper

Minimal diffeomorphism between hyperbolic surfaces with cone singularities

arXiv:1411.2656

Abstract

We prove the existence of a minimal diffeomorphism isotopic to the identity between two hyperbolic cone surfaces $(Σ, g_{1})$ and $(Σ, g_{2})$ when the cone angles of $g_{1}$ and $g_{2}$ are different and smaller than $π$ . When the cone angles of $g_{1}$ are strictly smaller than the ones of $g_{2}$ , this minimal diffeomorphism is unique.