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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



Harmonic maps with finite total energy

Authors: Shiu-Yuen Cheng, Luen-Fai Tam and Tom Y.-H. Wan
Journal: Proc. Amer. Math. Soc. 124 (1996), 275-284
MSC (1991): Primary 53C99; Secondary 31C05, 58E20
MathSciNet review: 1307503
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Abstract: We will give a criteria for a nonnegative subharmonic function with finite energy on a complete manifold to be bounded. Using this we will prove that if on a complete noncompact Riemannian manifold $M$, every harmonic function with finite energy is bounded, then every harmonic map with finite total energy from $M$ into a Cartan-Hadamard manifold must also have bounded image. No assumption on the curvature of $M$ is required. As a consequence, we will generalize some of the uniqueness results on homotopic harmonic maps by Schoen and Yau.

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Additional Information

Luen-Fai Tam

Tom Y.-H. Wan

Received by editor(s): July 28, 1994
Additional Notes: The first and the third authors are partially supported by Earmarked Grant, Hong Kong, and the second author is partially supported by NSF grant #DMS9300422.
Communicated by: Peter Li
Article copyright: © Copyright 1996 American Mathematical Society