{"paper":{"title":"Rectifiability of the singular set of multiple valued energy minimizing harmonic maps","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG"],"primary_cat":"math.AP","authors_text":"Daniele Valtorta, Jonas Hirsch, Salvatore Stuvard","submitted_at":"2017-08-07T13:44:04Z","abstract_excerpt":"In this paper we study the singular set of Dirichlet-minimizing $Q$-valued maps from $\\mathbb{R}^m$ into a smooth compact manifold $\\mathcal{N}$ without boundary. Similarly to what happens in the case of single valued minimizing harmonic maps, we show that this set is always $(m-3)$-rectifiable with uniform Minkowski bounds. Moreover, as opposed to the single valued case, we prove that the target $\\mathcal{N}$ being non-positively curved but not simply connected does not imply continuity of the map."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.02116","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"}