{"paper":{"title":"Integrability of Lawson-Osserman Cone and its Applications","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Lei Zhang, Qi Ding","submitted_at":"2026-05-24T07:45:13Z","abstract_excerpt":"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."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.24916","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2605.24916/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}