{"paper":{"title":"The Lavrentiev gap phenomenon for harmonic maps into spheres holds on a dense set of zero degree boundary data","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Katarzyna Mazowiecka, Pawe{\\l} Strzelecki","submitted_at":"2014-06-03T07:24:45Z","abstract_excerpt":"We prove that for each positive integer $N$ the set of smooth, zero degree maps $\\psi\\colon\\mathbb{S}^2\\to \\mathbb{S}^2$ which have the following three properties:\n  (1) there is a unique minimizing harmonic map $u\\colon \\mathbb{B}^3\\to \\mathbb{S}^2$ which agrees with $\\psi$ on the boundary of the unit ball;\n  (2) this map $u$ has at least $N$ singular points in $\\mathbb{B}^3$;\n  (3) the Lavrentiev gap phenomenon holds for $\\psi$, i.e., the infimum of the Dirichlet energies $E(w)$ of all smooth extensions $w\\colon \\mathbb{B}^3\\to\\mathbb{S}^2$ of $\\psi$ is strictly larger than the Dirichlet ene"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.0601","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":""},"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"}