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<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  Mⁿ, 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 = Sᵏ ⪫3,  we obtain a distinguished family of nonconstant harmonic maps M Sᵏ  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> .
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