Quantitative stratification and optimal regularity for harmonic almost complex structures
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866914207183667200 |
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| author | Guo, Chang-Yu Liu, Ming-Lun Xiang, Chang-Lin |
| author_facet | Guo, Chang-Yu Liu, Ming-Lun Xiang, Chang-Lin |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_16341 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Quantitative stratification and optimal regularity for harmonic almost complex structures Guo, Chang-Yu Liu, Ming-Lun Xiang, Chang-Lin Analysis of PDEs Differential Geometry 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. |
| title | Quantitative stratification and optimal regularity for harmonic almost complex structures |
| topic | Analysis of PDEs Differential Geometry |
| url | https://arxiv.org/abs/2512.16341 |