Nonstationary weak limit of a stationary harmonic map sequence

• Published in: Communications on pure and applied mathematics Vol. 56; no. 2; pp. 270 - 277
• Main Authors: Ding, Weiyue, Li, Jiayu, Li, Wei
• Format: Journal Article
• Language: English
• Published: New York Wiley Subscription Services, Inc., A Wiley Company 01.02.2003; Wiley
• Subjects: Exact sciences and technology; Functional analysis; Mathematical analysis; Mathematics; Ordinary differential equations; Sciences and techniques of general use; Hausdorff dimension; Stationary sequence; Riemann manifold; Sequence(mathematics); Harmonic analysis; Harmonic map; Compact manifold

Let M and N be two compact Riemannian manifolds. Let uk 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 H1,2 (M, N) as k → ∞. In this paper, we construct an example to show that the limit map u may not...