On the Harmonic Maps from R 2 into H 2

Jun-Min Lin
1990 Proceedings of the American Mathematical Society  
In this paper, we prove that normal.zed harmonic maps from R2 or R2\{0} into H2 are just geodesies on H2 and that the quasiconformal harmonic maps from R2 into H2 are constant maps. We prove also that the only solution to Aa = sinha on R2\{0} is the zero solution.
doi:10.2307/2048304 fatcat:p7hceams4bhnzhb76z6ok7fhym