Nonstationary weak limit of a stationary harmonic map sequence

Let M and N be two compact Riemannian manifolds. Let u_k be a sequence of stationary harmonic maps from M to N with bounded energies. We may assume that it converges weakly to a weakly harmonic map u in H^1,2 (M, N) as k → ∞. In this paper, we construct an example to show that the limit map u may not be stationary. © 2002 Wiley Periodicals, Inc.