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Transactions of the American Mathematical Society

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



Dirichlet problem at infinity for harmonic maps: rank one symmetric spaces

Author: Harold Donnelly
Journal: Trans. Amer. Math. Soc. 344 (1994), 713-735
MSC: Primary 58E20
MathSciNet review: 1250817
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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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