Stability of the equator map for the Hessian energy
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- by Min-Chun Hong and Bevan Thompson PDF
- Proc. Amer. Math. Soc. 135 (2007), 3163-3170 Request permission
Abstract:
In this paper we show that the equator map is a minimizer of the Hessian energy $H(u)=\int _{\Omega } |\bigtriangleup u|^{2} dx$ in $H^{2}(\Omega ;S^{n})$ for $n\geq 10$ and is unstable for $5\le n\le 9.$References
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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
- 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
- © Copyright 2007
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 135 (2007), 3163-3170
- MSC (2000): Primary 35J50
- DOI: https://doi.org/10.1090/S0002-9939-07-08950-2
- MathSciNet review: 2322746