{"paper":{"title":"Decay of excess for the abelian Higgs model","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.DG"],"primary_cat":"math.AP","authors_text":"Alessandro Pigati, Aria Halavati, Guido De Philippis","submitted_at":"2024-05-22T19:37:54Z","abstract_excerpt":"In this article we prove that entire critical points $(u,\\nabla)$ of the self-dual $U(1)$-Yang-Mills-Higgs functional $E_1$, with energy\n  $$E_1(u,\\nabla;B_R):=\\int_{B_R}\\left[|\\nabla u|^2+\\frac{(1-|u|^2)^2}{4}+|F_\\nabla|^2\\right]\\leq(2\\pi+\\tau(n)) \\omega_{n-2}R^{n-2}$$\n  for all $R>0$, have unique blow-down. Moreover, we show that they are two-dimensional in ambient dimension $2\\leq n\\leq4$, or in any dimension $n\\ge2$ assuming that $(u,\\nabla)$ is a local minimizer, thus establishing a co-dimension-two analogue of Savin's theorem. The main ingredient is an Allard-type improvement of flatness"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2405.13953","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/2405.13953/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"}