{"paper":{"title":"Energy Identity for Stationary Harmonic Maps","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG"],"primary_cat":"math.AP","authors_text":"Aaron Naber, Daniele Valtorta","submitted_at":"2024-01-04T12:53:37Z","abstract_excerpt":"In this paper we consider sequences $u_j:B_2\\subseteq M\\to N$ of stationary harmonic maps between smooth Riemannian manifolds with uniformly bounded energy $E[u_j]\\equiv \\int |\\nabla u_j|^2\\leq \\Lambda$ . After passing to a subsequence it is known one can limit $u_j\\to u:B_1\\to N$ with the associated defect measure $|\\nabla u_j|^2 dv_g \\to |\\nabla u|^2dv_g+\\nu$, where $\\nu = e(x)\\, H^{m-2}_S$ is an $m-2$ rectifiable measure \\cite{lin_stat}. For a.e. $x\\in S=\\operatorname{supp}(\\nu)$ one can produce a finite number of bubble maps $b_j:S^2\\to N$ by blowing up the sequence $u_j$ near $x$.\n  We pr"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2401.02242","kind":"arxiv","version":3},"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/2401.02242/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"}