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