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Stability of the equator map for the Hessian energy


Authors: Min-Chun Hong and Bevan Thompson
Journal: Proc. Amer. Math. Soc. 135 (2007), 3163-3170
MSC (2000): Primary 35J50
DOI: https://doi.org/10.1090/S0002-9939-07-08950-2
Published electronically: June 19, 2007
MathSciNet review: 2322746
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Abstract: In this paper we show that the equator map is a minimizer of the Hessian energy $ H(u)=\int _{\Omega } \vert\bigtriangleup u\vert^{2}\,dx$ in $ H^{2}(\Omega ;S^{n})$ for $ n\geq 10$ and is unstable for $ 5\le n\le 9.$


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Additional Information

Min-Chun Hong
Affiliation: Department of Mathematics, The University of Queensland, Brisbane, Queensland 4072, Australia
Email: hong@maths.uq.edu.au

Bevan Thompson
Affiliation: Department of Mathematics, The University of Queensland, Brisbane, Queensland 4072, Australia
Email: hbt@maths.uq.edu.au

DOI: https://doi.org/10.1090/S0002-9939-07-08950-2
Keywords: Biharmonic maps, Hessian energy, Dirichlet energy, minimizer, unstable
Received by editor(s): May 12, 2006
Published electronically: June 19, 2007
Additional Notes: The first author acknowledges the support of the Australian Research Council Discovery Grant DP0450140
Communicated by: Chuu-Lian Terng
Article copyright: © Copyright 2007 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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