Energy identity for $m$-harmonic maps

Abstract

For $m\ge 3$, let $M$, with dimension $m$, and $N$ be compact Riemannian manifolds without boundaries. We prove the energy identity (1.2) for a sequence of weakly convergent $m$-harmonic maps in $C^1(M,N)$. We also generalize the result to certain regular approximated $m$-harmonic maps whose tension fields are bounded in $L^{m\over m-1}$.