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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles 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 1.48 .

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Dirichlet problem at infinity for harmonic maps: rank one symmetric spaces
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by Harold Donnelly PDF
Trans. Amer. Math. Soc. 344 (1994), 713-735 Request permission

Abstract:

Given a symmetric space M, of rank one and noncompact type, one compactifies M by adding a sphere at infinity, to obtain a manifold $M\prime$ with boundary. If $\bar M$ is another rank one symmetric space, suppose that $f:\partial M\prime \to \partial \bar M\prime$ is a continuous map. The Dirichlet problem at infinity is to construct a proper harmonic map $u:M \to \bar M$ with boundary values f. This paper concerns existence, uniqueness, and boundary regularity for this Dirichlet problem.
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Additional Information
  • © Copyright 1994 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 344 (1994), 713-735
  • MSC: Primary 58E20
  • DOI: https://doi.org/10.1090/S0002-9947-1994-1250817-0
  • MathSciNet review: 1250817