A remark on instability of harmonic maps between spheres (Q1011637)
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scientific article; zbMATH DE number 5541999
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A remark on instability of harmonic maps between spheres |
scientific article; zbMATH DE number 5541999 |
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A remark on instability of harmonic maps between spheres (English)
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8 April 2009
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A harmonic map from the \(k\)-sphere to itself is a critical point of the Dirichlet functional. It is known that the first eigenvalue of the Hessian of the Dirichlet functional is bounded above by \(2-k\) [Xin, Eells-Lemaure, Urakema, Xin (1996)]. In this note, Nakajima utilizes a clever trick to prove that any harmonic map that attains this upper bound must be an isometry.
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harmonic maps
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instability
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spheres
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