Harmonic maps with finite total energy
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- by Shiu-Yuen Cheng, Luen-Fai Tam and Tom Y.-H. Wan PDF
- Proc. Amer. Math. Soc. 124 (1996), 275-284 Request permission
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.References
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Additional Information
- Luen-Fai Tam
- MR Author ID: 170445
- Email: ltam@math.uci.edu
- Tom Y.-H. Wan
- Email: tomwan@cuhk.hk
- 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
- © Copyright 1996 American Mathematical Society
- 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