Harmonic diffeomorphisms of the hyperbolic plane

Akutagawa, Kazuo

doi:10.1090/S0002-9947-1994-1147398-9

Harmonic diffeomorphisms of the hyperbolic plane
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by Kazuo Akutagawa

Trans. Amer. Math. Soc. 342 (1994), 325-342

DOI: https://doi.org/10.1090/S0002-9947-1994-1147398-9

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Abstract:

In this paper, we consider the Dirichlet problem at infinity for harmonic maps between the Poincaré model D of the hyperbolic plane ${\mathbb {H}^2}$, and solve this when given boundary data are ${C^4}$ immersions of $D(\infty )$, the boundary at infinity of D, to $D(\infty )$. Also, we present a construction of nonconformal harmonic diffeomorphisms of D, and give a complete description of the boundary behavior, including their first derivatives.

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