Lu's conjecture for minimal surfaces
Fuente:
arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| Soggetti: | |
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| _version_ | 1866918283342512128 |
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| author | Ding, Weiran Ge, Jianquan Li, Fagui Yang, Xize |
| author_facet | Ding, Weiran Ge, Jianquan Li, Fagui Yang, Xize |
| contents | After Chern's conjecture on the discreteness of the constant scalar curvatures of compact minimal submanifolds $M^n$ in unit spheres $\mathbb{S}^{n+q}$, Z. Q. Lu proposed a conjecture regarding the second gap, based on his ingenious refinement of the known first gap theorem. This refinement unifies Simons' first gap theorem for hypersurfaces with the corresponding theorems for high-codimensional submanifolds established by Yau, Shen, Li and Li, among others. In this paper, for arbitrary codimension, we prove Lu's conjecture for minimal 2-spheres, and for any minimal surfaces under some slight inequality conditions about the normal scalar curvature. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_07194 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Lu's conjecture for minimal surfaces Ding, Weiran Ge, Jianquan Li, Fagui Yang, Xize Differential Geometry 15A45, 15B57, 53C24, 53C42 After Chern's conjecture on the discreteness of the constant scalar curvatures of compact minimal submanifolds $M^n$ in unit spheres $\mathbb{S}^{n+q}$, Z. Q. Lu proposed a conjecture regarding the second gap, based on his ingenious refinement of the known first gap theorem. This refinement unifies Simons' first gap theorem for hypersurfaces with the corresponding theorems for high-codimensional submanifolds established by Yau, Shen, Li and Li, among others. In this paper, for arbitrary codimension, we prove Lu's conjecture for minimal 2-spheres, and for any minimal surfaces under some slight inequality conditions about the normal scalar curvature. |
| title | Lu's conjecture for minimal surfaces |
| topic | Differential Geometry 15A45, 15B57, 53C24, 53C42 |
| url | https://arxiv.org/abs/2601.07194 |