Weakly biharmonic maps from the ball to the sphere

Fardoun, A.;Montaldo, S.;Ratto, A.

2020-01-01

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Abstract

The aim of this paper is to investigate the existence of proper, weakly biharmonic maps within a family of rotationally symmetric maps ua : Bn → Sn, where Bn and Sn denote the Euclidean n-dimensional unit ball and sphere respectively. We prove that there exists a proper, weakly biharmonic map ua of this type if and only if n = 5 or n = 6. We shall also prove that these critical points are unstable.