{"paper":{"title":"Extendability of conformal structures on punctured surfaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Jingyi Chen, Yuxiang Li","submitted_at":"2015-09-27T07:40:14Z","abstract_excerpt":"For a smooth immersion $f$ from the punctured disk $D\\backslash\\{0\\}$ into $\\mathbb{R}^n$ extendable continuously at the puncture, if its mean curvature is square integrable and the measure of $f(D)\\cap B_{r_k}=o(r_k)$ for a sequence $r_k\\to 0$, we show that the Riemannian surface $(D_r\\backslash\\{0\\},g)$ where $g$ is the induced metric is conformally equivalent to the unit Euclidean punctured disk, for any $r\\in(0,1)$. For a locally $W^{2,2}$ Lipschitz immersion $f$ from the punctured disk $D_2\\backslash\\{0\\}$ into $\\mathbb{R}^n$, if $\\|\\nabla f\\|_{L^\\infty}$ is finite and the second fundamen"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.08061","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"}