Harmonic maps with finite total energy
Authors:
ShiuYuen Cheng, LuenFai Tam and Tom Y.H. Wan
Journal:
Proc. Amer. Math. Soc. 124 (1996), 275284
MSC (1991):
Primary 53C99; Secondary 31C05, 58E20
MathSciNet review:
1307503
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Abstract 
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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 , every harmonic function with finite energy is bounded, then every harmonic map with finite total energy from into a CartanHadamard manifold must also have bounded image. No assumption on the curvature of 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
LuenFai Tam
Email:
ltam@math.uci.edu
Tom Y.H. Wan
Email:
tomwan@cuhk.hk
DOI:
http://dx.doi.org/10.1090/S000299399603170X
PII:
S 00029939(96)03170X
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
