{"paper":{"title":"Uniqueness of degree-one Ginzburg-Landau vortex in the unit ball in dimensions $N \\geq 7$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.AP","authors_text":"Arghir Zarnescu, Luc Nguyen, Radu Ignat, Valeriy Slastikov","submitted_at":"2018-06-27T13:07:12Z","abstract_excerpt":"For $\\epsilon>0$, we consider the Ginzburg-Landau functional for $\\mathbb R^N$-valued maps defined in the unit ball $B^N\\subset \\mathbb R^N$ with the vortex boundary data $x$ on $\\partial B^N$. In dimensions $N\\geq 7$, we prove that for every $\\epsilon>0$, there exists a unique global minimizer $u_\\epsilon$ of this problem; moreover, $u_\\epsilon$ is symmetric and of the form $u_\\epsilon(x)=f_\\epsilon(|x|)\\frac{x}{|x|}$ for $x\\in B^N$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.10453","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"}