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http://dx.doi.org/10.4134/JKMS.2005.42.3.543

ASYMPTOTIC DIRICHLET PROBLEM FOR HARMONIC MAPS ON NEGATIVELY CURVED MANIFOLDS  

KIM SEOK WOO (Department of Mathematics Education Konkuk University)
LEE YONG HAH (Department of Mathematics Education Ewha Womans University)
Publication Information
Journal of the Korean Mathematical Society / v.42, no.3, 2005 , pp. 543-553 More about this Journal
Abstract
In this paper, we prove the existence of nonconstant bounded harmonic maps on a Cartan-Hadamard manifold of pinched negative curvature by solving the asymptotic Dirichlet problem. To be precise, given any continuous data f on the boundary at infinity with image within a ball in the normal range, we prove that there exists a unique harmonic map from the manifold into the ball with boundary value f.
Keywords
asymptotic Dirichlet Problem; harmonic maps;
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