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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2605.24916 |
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| _version_ | 1866916042895261696 |
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| author | Ding, Qi Zhang, Lei |
| author_facet | Ding, Qi Zhang, Lei |
| contents | In this paper, we characterize all eigenfunctions corresponding to nonpositive eigenvalues of the Jacobi operator of the link $M$ of the Lawson-Osserman cone $\mathbf{C}$ in $\mathbb{R}^7$. In particular, we prove that $\mathbf{C}$ is integrable, i.e., all Jacobi fields on $\mathbf{C}$ of homogeneous degree 1 and 0, are generated by rotations and translations in $\mathbb{R}^7$. As applications, we prove that $M$ is rigid as minimal submanifolds in $\mathbb{S}^6$, and derive the optimal decay order for minimal submanifolds in $\mathbb{R}^7$ asymptotic to $\mathbf{C}$ at infinity. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_24916 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Integrability of Lawson-Osserman Cone and its Applications Ding, Qi Zhang, Lei Differential Geometry In this paper, we characterize all eigenfunctions corresponding to nonpositive eigenvalues of the Jacobi operator of the link $M$ of the Lawson-Osserman cone $\mathbf{C}$ in $\mathbb{R}^7$. In particular, we prove that $\mathbf{C}$ is integrable, i.e., all Jacobi fields on $\mathbf{C}$ of homogeneous degree 1 and 0, are generated by rotations and translations in $\mathbb{R}^7$. As applications, we prove that $M$ is rigid as minimal submanifolds in $\mathbb{S}^6$, and derive the optimal decay order for minimal submanifolds in $\mathbb{R}^7$ asymptotic to $\mathbf{C}$ at infinity. |
| title | Integrability of Lawson-Osserman Cone and its Applications |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/2605.24916 |