eprintid: 10194583 rev_number: 22 eprint_status: archive userid: 699 dir: disk0/10/19/45/83 datestamp: 2024-07-16 14:33:52 lastmod: 2024-07-16 15:09:34 status_changed: 2024-07-16 14:33:52 type: article metadata_visibility: show sword_depositor: 699 creators_name: Karpukhin, Mikhail creators_name: Stern, Daniel title: Existence of harmonic maps and eigenvalue optimization in higher dimensions ispublished: pub divisions: UCL divisions: B04 divisions: C06 divisions: F59 note: © The Author(s), 2024. This is an Open Access article distributed under the terms of the Creative Commons Attribution Licence (CC BY 4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. https://creativecommons.org/licenses/by/4.0/ 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. In 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. Furthermore, 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 date: 2024-05 date_type: published publisher: Springer Science and Business Media LLC official_url: https://doi.org/10.1007/s00222-024-01247-3 oa_status: green full_text_type: pub language: eng primo: open primo_central: open_green verified: verified_manual elements_id: 2297059 doi: 10.1007/s00222-024-01247-3 lyricists_name: Karpukhin, Mikhail lyricists_id: MKARP96 actors_name: Karpukhin, Mikhail actors_id: MKARP96 actors_role: owner full_text_status: public publication: Inventiones Mathematicae volume: 236 pagerange: 713-778 issn: 0020-9910 citation: Karpukhin, Mikhail; Stern, Daniel; (2024) Existence of harmonic maps and eigenvalue optimization in higher dimensions. Inventiones Mathematicae , 236 pp. 713-778. 10.1007/s00222-024-01247-3 <https://doi.org/10.1007/s00222-024-01247-3>. Green open access document_url: https://discovery.ucl.ac.uk/id/eprint/10194583/1/Karpukhin_s00222-024-01247-3.pdf