On the Jäger-Kaul theorem concerning harmonic maps

Min Chun Hong

doi:10.1016/S0294-1449(99)00103-1

On the Jäger-Kaul theorem concerning harmonic maps

Min Chun Hong^*

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

9 Citations (Scopus)

Abstract

In 1983, Jäger and Kaul proved that the equator map u*(x) = (x/|x|, 0) : Bⁿ → Sⁿ is unstable for 3 ≤ n ≤ 6 and a minimizer for the energy functional E(u, Bⁿ) = ∫_Bn |∇u|²dx in the class H^1,2(Bⁿ, Sⁿ) with u = u* on ∂ Bⁿ when n ≥ 7. In this paper, we give a new and elementary proof of this Jäger-Kaul result. We also generalize the Jäger-Kaul result to the case of p-harmonic maps.

Original language	English
Pages (from-to)	35-46
Number of pages	12
Journal	Annales de l'Institut Henri Poincare (C) Analyse Non Lineaire
Volume	17
Issue number	1
DOIs	https://doi.org/10.1016/S0294-1449(99)00103-1
Publication status	Published - Jan 2000

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abstract = "In 1983, J{\"a}ger and Kaul proved that the equator map u*(x) = (x/|x|, 0) : Bn → Sn is unstable for 3 ≤ n ≤ 6 and a minimizer for the energy functional E(u, Bn) = ∫Bn |∇u|2dx in the class H1,2(Bn, Sn) with u = u* on ∂ Bn when n ≥ 7. In this paper, we give a new and elementary proof of this J{\"a}ger-Kaul result. We also generalize the J{\"a}ger-Kaul result to the case of p-harmonic maps.",

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AB - In 1983, Jäger and Kaul proved that the equator map u*(x) = (x/|x|, 0) : Bn → Sn is unstable for 3 ≤ n ≤ 6 and a minimizer for the energy functional E(u, Bn) = ∫Bn |∇u|2dx in the class H1,2(Bn, Sn) with u = u* on ∂ Bn when n ≥ 7. In this paper, we give a new and elementary proof of this Jäger-Kaul result. We also generalize the Jäger-Kaul result to the case of p-harmonic maps.

UR - https://www.scopus.com/pages/publications/0013198067

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IS - 1

ER -

On the Jäger-Kaul theorem concerning harmonic maps

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