Minimal diffeomorphism between hyperbolic surfaces with cone singularities

2014/11/10 by Jérémy Toulisse, Toulisse, Jérémy
Mathematics · #30F60 #53A10 #58E20 #Analytic and geometric function theory #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Mathematical Dynamics and Fractals

paper · pdf · doi:10.48550/arxiv.1411.2656

openalex publication_date 2014/11/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove the existence of a minimal diffeomorphism isotopic to the identity between two hyperbolic cone surfaces (Σ,g₁) and (Σ,g₂) when the cone angles of g₁ and g₂ are different and smaller than π. When the cone angles of g₁ are strictly smaller than the ones of g₂, this minimal diffeomorphism is unique.

Citations

• Harmonic maps into conic surfaces with cone angles less than 2π
• Harmonic Mappings of Riemannian Manifolds
• On the Renormalized Volume of Hyperbolic 3-Manifolds

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