On the Jäger-Kaul theorem concerning harmonic maps

Research Report MRR96-050

On the Jäger-Kaul theorem concerning harmonic maps

Min-Chun Hong

Abstract: In 1983, Jäger-Kaul proved that the equator map $u^* (x) = ({\frac{x}{|x|}}, 0) \ : \ B^n \rightarrow S^n$ is unstable for $3 \leq n \leq 6$ and attains the minimum of the energy functional $E (u, B^n) = \int_{B^n} | \nabla u|^2 dx$ in the class $H^{1, 2} (B^{n}, S^{n})$ with

on $\partial B^{n}$ when $n \geq 7$ . 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.

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