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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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Harmonic diffeomorphisms of the hyperbolic plane
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by Kazuo Akutagawa PDF
Trans. Amer. Math. Soc. 342 (1994), 325-342 Request permission

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
  • © Copyright 1994 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 342 (1994), 325-342
  • MSC: Primary 58E20; Secondary 58G20
  • DOI: https://doi.org/10.1090/S0002-9947-1994-1147398-9
  • MathSciNet review: 1147398