Polynomial growth harmonic maps on complete Riemannian manifolds
Bull. Korean Math. Soc. 2004 Vol. 41, No. 3, 521-540
Published online September 1, 2004
Yong Hah Lee
Ewha Womans University
Abstract : In this paper, we give a sharp estimate on the cardinality of the set generating the convex hull containing the image of harmonic maps with polynomial growth rate on a certain class of manifolds into a Cartan-Hadamard manifold with sectional curvature bounded by two negative constants. We also describe the asymptotic behavior of harmonic maps on a complete Riemannian manifold into a regular ball in terms of massive subsets, in the case when the space of bounded harmonic functions on the manifold is finite dimensional.
Keywords : polynomial growth harmonic map, convex hull
MSC numbers : 31C05, 53C21, 58E20
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