{"paper":{"title":"On $\\delta$-Stable Minimal Hypersurfaces in $\\mathbb{R}^{n+1}$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.DG","authors_text":"Gaoming Wang, Haizhong Li, Han Hong","submitted_at":"2024-07-03T15:49:34Z","abstract_excerpt":"In this paper, we extend several results established for stable minimal hypersurfaces to $\\delta$-stable minimal hypersurfaces. These include the regularity and compactness theorems for immersed $\\delta$-stable minimal hypersurfaces in $\\mathbb{R}^{n+1}$ when $n \\geq 3$ and $\\delta > \\frac{n-2}{n}$, as well as the $\\delta$-stable Bernstein theorem for $n=3$ and $n=4$ for properly immersion. The range of $\\delta$ is optimal, as the $n$-dimensional catenoid in $\\mathbb{R}^{n+1}$ is $\\frac{n-2}{n}$-stable."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2407.03222","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/2407.03222/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"}