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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Harmonic diffeomorphisms of the hyperbolic plane


Author: Kazuo Akutagawa
Journal: Trans. Amer. Math. Soc. 342 (1994), 325-342
MSC: Primary 58E20; Secondary 58G20
MathSciNet review: 1147398
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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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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1994-1147398-9
PII: S 0002-9947(1994)1147398-9
Article copyright: © Copyright 1994 American Mathematical Society