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Mappings of nonpositively curved manifolds

Published online by Cambridge University Press:  22 January 2016

Samuel I. Goldberg*
Affiliation:
University of Illinois
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In recent papers with S. S. Chern [3] and T.Ishihara [4], the author studied both the volume—and distance—decreasing properties of harmonic mappings thereby obtaining real analogues and generalizations of the classical Schwarz-Ahlfors lemma, as well as Liouville’s theorem and the little Picard theorem. The domain M in the first case was the open ball with the hyperbolic metric of constant negative curvature, and the target was a negatively curved Riemannian manifold with sectional curvature bounded away from zero. In this paper, it is shown that M may be taken to be any complete Riemannian manifold of non-positive curvature.

Type
Research Article
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1976

References

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[3] Chern, S. S. and Goldberg, S. I., On the volume-decreasing property of a class of real harmonic mappings, Amer. J. Math. 97 (1975), 133147.Google Scholar
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[5] Goldberg, S. I. and Ishihara, T., Harmonic quasiconformal mappings of Riemannian manifolds, Amer. J. Math., to appear.Google Scholar
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