{"paper":{"title":"The singular set of minimal surfaces near polyhedral cones","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Luca Spolaor, Maria Colombo, Nick Edelen","submitted_at":"2017-09-28T13:46:11Z","abstract_excerpt":"We adapt the method of Simon [JDG '93] to prove a $C^{1,\\alpha}$-regularity theorem for minimal varifolds which resemble a cone $\\bf{C}_0^2$ over an equiangular geodesic net. For varifold classes admitting a \"no-hole\" condition on the singular set, we additionally establish $C^{1,\\alpha}$-regularity near the cone $\\bf{C}_0^2 \\times \\mathbb R^m$. Combined with work of Allard [Ann. of Math. '72], Simon [JDG '93], Taylor [Ann. of Math. '76], and Naber-Valtorta [Ann. of Math. '17], our result implies a $C^{1,\\alpha}$-structure for the top three strata of minimizing clusters and size-minimizing cur"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.09957","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":""},"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"}