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

Donnelly, Harold

doi:10.1090/S0002-9947-1994-1250817-0

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

Trans. Amer. Math. Soc. 344 (1994), 713-735

DOI: https://doi.org/10.1090/S0002-9947-1994-1250817-0

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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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