{"paper":{"title":"Singular Limits for Three-Dimensional Global Minimizers of Ginzburg--Landau-Type Functionals: Uniform Estimates and Singular Sets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Giacomo Canevari, Haotong Fu, Wei Wang","submitted_at":"2026-06-26T03:32:29Z","abstract_excerpt":"We study the asymptotic behavior of global minimizers of a Ginzburg--Landau-type functional with general compact vacuum manifold $\\mathcal{N}$ on bounded domains in $\\mathbb{R}^3$, in the regime where the energy grows at a logarithmic rate. We show that the normalized energy measures converge, up to a subsequence, to a measure supported on a finite union of closed line segments connecting prescribed singularities on the boundary. The limit map is a harmonic map valued locally by minimizing $\\mathcal{N}$ away from this singular set. We also establish uniform $W^{1,q}$-estimates with $ q\\in(1,2)"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.27691","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2606.27691/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}