## 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