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Harmonic Diffeomorphisms between Complete Riemann Surfaces of Negative Curvature

Harmonic Diffeomorphisms between Complete Riemann Surfaces of Negative Curvature

Consider two open Riemannian surfaces (M 2 , g 0 ), (M 2 , g 1 ), a curve {gt} 0≤t≤1 in the Sobolev topology, Kg t ≡ -1, inf σ(∆ 0 (gt)) > 0, r inj (gt) > 0, 0 ≤ t ≤ 1.We prove that there exists a …