Harmonic diffeomorphisms of a surface are energy minimizing according to a result of J. M. Coron and the author [Compos. Math. 69, No.2, 175-228 (1989; Zbl 0686.58012)]. Here the author shows that, for , the identity map of the unit ball onto itself with canonical metric on the domain and ‘SO(m)-equivariant metric’ h on the range is energy minimizing (provided it is harmonic) in the Sobolev space of to
SO(m)-equivariance means that
where are continuous. The proof is based on a comparison with a null Lagrangian.