Abstract: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.
| Comments: | 37 pages, comments are welcome! |
| Subjects: | Differential Geometry (math.DG) |
| Cite as: | arXiv:2605.24916 [math.DG] |
| (or arXiv:2605.24916v1 [math.DG] for this version) | |
| https://doi.org/10.48550/arXiv.2605.24916 arXiv-issued DOI via DataCite (pending registration) |
From: Lei Zhang [view email]
[v1]
Sun, 24 May 2026 07:45:13 UTC (46 KB)
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