Harmonic diffeomorphisms between complete surfaces (Q1355704)

Theorem: Let \(\varphi: M\to N\) be a diffeomorphism of finite energy between two complete Riemannian surfaces of genera \(\geq 1\) and of finite total curvature. Then \(\varphi\) can be deformed to a harmonic diffeomorphism of least energy in its homotopy class. The case where \(M\) and \(N\) are compact is due to \textit{J. Jost} and \textit{R. Schoen} [Invent. Math. 66, 353-359 (1982; Zbl 0488.58009)]. Proof of the Theorem uses their replacement argument.