On the harmonic maps from $\textbf {R}^ 2$ into $H^ 2$
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- by Jun Min Lin PDF
- Proc. Amer. Math. Soc. 108 (1990), 521-527 Request permission
Abstract:
In this paper, we prove that normalized harmonic maps from ${{\mathbf {R}}^2}$ or ${{\mathbf {R}}^2}\backslash \{ 0\}$ into ${H^2}$ are just geodesies on ${H^2}$ and that the quasiconformal harmonic maps from ${{\mathbf {R}}^2}$ into ${H^2}$ are constant maps. We prove also that the only solution to $\Delta \alpha = \sinh \alpha$ on ${{\mathbf {R}}^2}\backslash \{ 0\}$ is the zero solution.References
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Additional Information
- © Copyright 1990 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 108 (1990), 521-527
- MSC: Primary 58E20; Secondary 30C60, 35Q99
- DOI: https://doi.org/10.1090/S0002-9939-1990-0975649-1
- MathSciNet review: 975649