{"paper":{"title":"Weak convergence of branched conformal immersions with uniformly bounded areas and Willmore energies","license":"http://creativecommons.org/publicdomain/zero/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Guodong Wei","submitted_at":"2018-01-21T08:22:17Z","abstract_excerpt":"In this paper, we firstly extend Theorem 5.1.1 in \\cite {Helein} due to H\\'elein to a rescaled branched conformal immersed sequence(c.f. Theorem 1.5). By virtue of this local convergence theorem, we study the blowup behavior of a sequence of branched conformal immersions of closed Riemannian surface in $\\mathbb{R}^{n}$ with uniformly bounded areas and Willmore energies. Furthermore, we prove that the integral identity of Gauss curvature is true."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.06786","kind":"arxiv","version":4},"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"}