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arXiv · 2512.16341

Quantitative stratification and optimal regularity for harmonic almost complex structures

Chang-Yu Guo·Ming-Lun Liu·Chang-Lin Xiang
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Abstract

In a recent interesting work [15], W.Y. He established the important partial regularity theory and the almost optimal higher regularity theory for energy minimizing harmonic almost complex structures. Based on a new observation on the structure of equations, we give an easier new proof of the partial regularity theorem, and adapting the powerful quantitative stratification method of Naber-Valtorta [22], we further prove the rectifiability of singular stratum of energy minimizing harmonic almost complex structures. Based on this, we establish an optimal regularity theory, which improves the corresponding result of He.

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Chang-Yu Guo, Ming-Lun Liu, Chang-Lin Xiang. 2025-12-18. Quantitative stratification and optimal regularity for harmonic almost complex structures. https://arxiv.org/abs/2512.16341

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