»ã±¨±êÌâ (Title)£ººÍгӳÉäµÄÕýÔòÐÔÀíÂÛ¼°Íƹã

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»ã±¨¹¦·ò (Time)£º2024Äê9ÔÂ27ÈÕ£¨ÖÜÎ壩 14:00

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»ã±¨ÌáÒª£ºIn this talk, I will give an overview of the regularity theory concerning the singular set of harmonic mappings into closed manifolds. In particular, we recall the classical stratification theory for harmonic mappings based on the fundamental work of Schoen-Uhlenbeck [J. Diff. Geom. 1982], L. Simon [CVPDE 1995] and F.H. Lin [Ann. Math. 1999]. Then we introduce the quantitative stratification theory developed by Cheeger-Naber [Invent. Math. 2013], and by Naber-Valtorta [Ann. Math. 2017, arXiv 2024]. Finally, we briefly discuss the natural extension to half/bi-harmonic mappings and almost complex structure. The talk is based on recent joint works with Guichun Jiang, Changyou Wang, Changlin Xiang and Gaofeng Zheng.