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Limits of alpha-harmonic maps
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Lamm, Tobias, Malchiodi, Andrea and Micallef, Mario (2020) Limits of alpha-harmonic maps. Journal of Differential Geometry, 116 (2). pp. 321-348. doi:10.4310/jdg/1603936814 ISSN 0022-040X.
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Official URL: https://doi.org/10.4310/jdg/1603936814
Abstract
Critical points of approximations of the Dirichlet energy à la Sacks-Uhlenbeck are known to converge to harmonic maps in a suitable sense. However, we show that not every harmonic map can be approximated by critical points of such perturbed energies. Indeed, we prove that constant maps and maps of the form u R (x) =Rx,R∈O(3), are the only critical points of E α for maps from S2 to S2 whose α-energy lies below some threshold. In particular, nontrivial dilations (which are harmonic) cannot arise as strong limits of α-harmonic maps.
| Item Type: | Journal Article | ||||||
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| Subjects: | Q Science > QA Mathematics | ||||||
| Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||||
| Library of Congress Subject Headings (LCSH): | Harmonic maps | ||||||
| Journal or Publication Title: | Journal of Differential Geometry | ||||||
| Publisher: | Lehigh University * Department of Mathematics | ||||||
| ISSN: | 0022-040X | ||||||
| Official Date: | October 2020 | ||||||
| Dates: |
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| Volume: | 116 | ||||||
| Number: | 2 | ||||||
| Page Range: | pp. 321-348 | ||||||
| DOI: | 10.4310/jdg/1603936814 | ||||||
| Status: | Peer Reviewed | ||||||
| Publication Status: | Published | ||||||
| Access rights to Published version: | Restricted or Subscription Access | ||||||
| Copyright Holders: | Copyright © 2020 Lehigh University | ||||||
| Date of first compliant deposit: | 11 February 2019 | ||||||
| Date of first compliant Open Access: | 11 February 2019 | ||||||
| RIOXX Funder/Project Grant: |
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