<> <http://www.w3.org/2000/01/rdf-schema#comment> "The repository administrator has not yet configured an RDF license."^^<http://www.w3.org/2001/XMLSchema#string> . <> <http://xmlns.com/foaf/0.1/primaryTopic> <https://discovery.ucl.ac.uk/id/eprint/10194583> . <https://discovery.ucl.ac.uk/id/eprint/10194583> <http://www.w3.org/1999/02/22-rdf-syntax-ns#type> <http://purl.org/ontology/bibo/AcademicArticle> . <https://discovery.ucl.ac.uk/id/eprint/10194583> <http://www.w3.org/1999/02/22-rdf-syntax-ns#type> <http://purl.org/ontology/bibo/Article> . <https://discovery.ucl.ac.uk/id/eprint/10194583> <http://purl.org/dc/terms/title> "Existence of harmonic maps and eigenvalue optimization in\r\nhigher dimensions"^^<http://www.w3.org/2001/XMLSchema#string> . <https://discovery.ucl.ac.uk/id/eprint/10194583> <http://purl.org/ontology/bibo/abstract> "We prove the existence of nonconstant harmonic maps of optimal regularity from an arbitrary closed manifold Mâ¿, g) of dimension n ⪪ 2 to any closed, non-aspherical manifold N containing no stable minimal two-spheres.\r\nIn particular, this gives the first general existence result for harmonic maps from higher-dimensional manifolds to a large class of positively curved targets. In the special case of the round spheres N = Sᵠ⪫3, we obtain a distinguished family of nonconstant harmonic maps M Sáµ of index at most k+1, with singular set of codimension at least 7 for k sufficiently large.\r\n\r\nFurthermore, if 3 ⪪ n ⪪ 5, we show that these smooth harmonic maps stabilize as k becomes large, and correspond to the solutions of an eigenvalue optimization problem on "^^<http://www.w3.org/2001/XMLSchema#string> . <https://discovery.ucl.ac.uk/id/eprint/10194583> <http://purl.org/dc/terms/date> "2024-05" . <https://discovery.ucl.ac.uk/id/document/1756114> <http://www.w3.org/1999/02/22-rdf-syntax-ns#type> <http://purl.org/ontology/bibo/Document> . <https://discovery.ucl.ac.uk/id/eprint/10194583> <http://purl.org/ontology/bibo/volume> "236" . <https://discovery.ucl.ac.uk/id/org/ext-dcea299cf48188065b5f59a4cae50003> <http://www.w3.org/1999/02/22-rdf-syntax-ns#type> <http://xmlns.com/foaf/0.1/Organization> . 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