A counterexample to the energy identity for sequences of $\alpha$-harmonic maps

Yuxiang Li and Youde Wang

Vol. 274 (2015), No. 1, 107–123

DOI: 10.2140/pjm.2015.274.107

Abstract

We construct a closed Riemannian manifold $\left(N,h\right)$ and a sequence of $\alpha$-harmonic maps from $S^2$ into $N$ with uniformly bounded energy such that the energy identity for this sequence is not true.

Keywords

$\alpha$-harmonic map, energy identity

Mathematical Subject Classification 2010

Primary: 58E20

Secondary: 35Q60

Milestones

Received: 29 September 2013

Revised: 4 January 2014

Accepted: 31 January 2014

Published: 2 March 2015