Stability of the equator map for the Hessian energy

Hong, Min-Chun; Thompson, Bevan

doi:10.1090/S0002-9939-07-08950-2

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 $5\le n\le 9.$

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