{"paper":{"title":"Rectifiable-Reifenberg and the Regularity of Stationary and Minimizing Harmonic Maps","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.DG","authors_text":"Aaron Naber, Daniele Valtorta","submitted_at":"2015-04-08T17:32:34Z","abstract_excerpt":"In this paper we study the regularity of stationary and minimizing harmonic maps $f:B_2(p)\\subseteq M\\to N$ between Riemannian manifolds. If $S^k(f)\\equiv\\{x\\in M: \\text{ no tangent map at $x$ is }k+1\\text{-symmetric}\\}$ is $k^{th}$-stratum of the singular set of $f$, then it is well known that $\\dim S^k\\leq k$, however little else about the structure of $S^k(f)$ is understood in any generality. Our first result is for a general stationary harmonic map, where we prove that $S^k(f)$ is $k$-rectifiable.\n  In the case of minimizing harmonic maps we go further, and prove that the singular set $S(f"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.02043","kind":"arxiv","version":5},"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"}