Gradient estimates and blow-up analysis for stationary harmonic maps

• 成果类型: Article
• 署名作者: Lin, FH
• 刊物名称: ANNALS OF MATHEMATICS
• ISSN/ISSBN: 0003-486X
• DOI: 10.2307/121073
• 发表日期: 1999
• 页码: 785-829
• 关键词: energy minimizing maps; SINGULAR SET; REGULARITY; mappings; spheres

摘要

For stationary harmonic maps between Riemannian manifolds, we provide a necessary and sufficient condition for the uniform interior and boundary gradient estimates in terms of the total energy of maps. We also show that if analytic target manifolds do not carry any harmonic S-2, then the singular sets of stationary maps are m less than or equal to n - 4 rectifiable. Both of these results follow from a general analysis on the defect measures and energy concentration sets associated with a weakly converging sequence of stationary harmonic maps.