Minimal diffeomorphism between hyperbolic surfaces with cone singularities

摘要

We prove the existence of a minimal diffeomorphism isotopic to the identity between two hyperbolic cone surfaces (Sigma, g(1)) and (Sigma, g(2)) when the cone angles of g(1) and g(2) are different and smaller than pi. When the cone angles of g(1) are strictly smaller than the ones of g(2), this minimal diffeomorphism is unique.