AI 中文总结
本文综述极小调和映射正则性理论的核心结果，涵盖变分、正则性定理、爆破与奇异集分析，并延伸至平稳情形及近期进展。
AI 中文摘要
我们介绍了调和映射正则性理论中的各种经典基础结果，重点关注能量极小调和映射。主题包括内变分与外变分、单调性恒等式、ε-正则性定理、爆破与切映射、奇异集的维数估计与分层。我们还讨论了平稳调和映射的类似理论，并提及一些重要的近期进展。
英文摘要
We introduce various classical, foundational results on the regularity theory of harmonic maps, with focuses on the energy minimising harmonic maps. Topics include inner and outer variations, the monotonicity identity, the $\varepsilon$-regularity theorem, blow-ups and tangent maps, and the dimension estimate and stratification of singular sets. We also discuss the analogous theory for stationary harmonic maps and mention some significant recent developments.
CommentsNotes for minicourse delivered at the Winter School on Geometric Measure Theory Rectifiability vs. Pure Unrectifiability
