{"paper":{"title":"Global regularity for minimal sets near a $\\T$ set and counterexamples","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Xiangyu Liang","submitted_at":"2011-12-15T16:48:54Z","abstract_excerpt":"We discuss the global regularity for 2 dimensional minimal sets that are near a $\\T$ set, that is, whether every global minimal set in $\\R^n$ that looks like a $\\T$ set at infinity is a $\\T$ set or not. The main point is to use the topological properties of a minimal set at large scale to control its topology at smaller scales. This is the idea to prove that all 1-dimensional Almgren-minimal sets in $\\R^n$, and all 2-dimensional Mumford-Shah minimal sets in $\\R^3$ are cones. In this article we discuss two types of 2-dimensional minimal sets: Almgren-minimal set in $\\R^3$ whose blow-in limit is"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1112.3565","kind":"arxiv","version":2},"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"}