Pacheco, R and Wood, JC orcid.org/0000-0003-0024-4673 (2023) Diagrams and harmonic maps, revisited. Annali di Matematica Pura ed Applicata, 202. pp. 1051-1085. ISSN 0373-3114
Abstract
We extend many known results for harmonic maps from the 2-sphere into a Grassmannian to harmonic maps of finite uniton number from an arbitrary Riemann surface. Our method relies on a new theory of nilpotent cycles arising from the diagrams of F.E. Burstall and the second author associated to such harmonic maps; these properties arise from a criterion for finiteness of the uniton number found recently by the authors with A. Aleman. Applications include a new classification result on minimal surfaces of constant curvature and a constancy result for finite type harmonic maps.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © Fondazione Annali di Matematica Pura ed Applicata and Springer-Verlag GmbH Germany, part of Springer Nature 2022. This is an author produced version of an article published in Annali di Matematica Pura ed Applicata. Uploaded in accordance with the publisher's self-archiving policy. |
Keywords: | Harmonic maps; Grassmannian manifolds; Riemann surfaces; Shift-invariant subspaces; Finite uniton number; Finite type |
Dates: |
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Institution: | The University of Leeds |
Academic Units: | The University of Leeds > Faculty of Engineering & Physical Sciences (Leeds) > School of Mathematics (Leeds) > Pure Mathematics (Leeds) |
Depositing User: | Symplectic Publications |
Date Deposited: | 11 Oct 2022 12:02 |
Last Modified: | 07 Nov 2023 01:13 |
Published Version: | https://link.springer.com/article/10.1007/s10231-0... |
Status: | Published |
Publisher: | Springer |
Identification Number: | 10.1007/s10231-022-01271-1 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:191424 |