{"paper":{"title":"Minimal submanifolds from the abelian Higgs model","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.DG","authors_text":"Alessandro Pigati, Daniel Stern","submitted_at":"2019-05-31T17:23:47Z","abstract_excerpt":"Given a Hermitian line bundle $L\\to M$ over a closed, oriented Riemannian manifold $M$, we study the asymptotic behavior, as $\\epsilon\\to 0$, of couples $(u_\\epsilon,\\nabla_\\epsilon)$ critical for the rescalings \\begin{align*} &E_\\epsilon(u,\\nabla)=\\int_M\\Big(|\\nabla u|^2+\\epsilon^2|F_\\nabla|^2+\\frac{1}{4\\epsilon^2}(1-|u|^2)^2\\Big) \\end{align*} of the self-dual Yang-Mills-Higgs energy, where $u$ is a section of $L$ and $\\nabla$ is a Hermitian connection on $L$ with curvature $F_{\\nabla}$.\n  Under the natural assumption $\\limsup_{\\epsilon\\to 0}E_\\epsilon(u_\\epsilon,\\nabla_\\epsilon)<\\infty$, we "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1905.13726","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"}