On stable quasi-harmonic maps and Liouville type theorems

Authors:
Deliang Hsu and Chunqin Zhou

Journal:
Proc. Amer. Math. Soc. **130** (2002), 3415-3422

MSC (2000):
Primary 58G30, 35B05

Published electronically:
May 8, 2002

MathSciNet review:
1913022

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Abstract: We consider Liouville type problems of stable quasi-harmonic maps, by ``stable'' we mean that the second variation of quasi-energy functional is nonnegative, and we prove that the stable quasi-harmonic maps must be constant under some geometry conditions.

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Additional Information

**Deliang Hsu**

Affiliation:
Department of Applied Mathematics, Shanghai Jiao Tong University, Shanghai 200240, People’s Republic of China

Email:
hsudl@online.sh.cn

**Chunqin Zhou**

Affiliation:
Department of Applied Mathematics, Shanghai Jiao Tong University, Shanghai 200240, People’s Republic of China

DOI:
https://doi.org/10.1090/S0002-9939-02-06499-7

Keywords:
Quasi-harmonic map,
stableness,
Liouville type theorems

Received by editor(s):
April 19, 2000

Received by editor(s) in revised form:
June 25, 2001

Published electronically:
May 8, 2002

Additional Notes:
The first author was supported by NSF of Shanghai Jiao Tong University

Communicated by:
Bennett Chow

Article copyright:
© Copyright 2002
American Mathematical Society