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

DOI:
https://doi.org/10.1090/S0002-9939-96-03170-X

MathSciNet review:
1307503

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Abstract | References | Similar Articles | Additional Information

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 Cartan-Hadamard 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

**Luen-Fai Tam**

Email:
ltam@math.uci.edu

**Tom Y.-H. Wan**

Email:
tomwan@cuhk.hk

DOI:
https://doi.org/10.1090/S0002-9939-96-03170-X

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