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A Factorization Theorem for Harmonic Maps

Sagman, Nathaniel (2021) A Factorization Theorem for Harmonic Maps. Journal of Geometric Analysis, 31 (12). pp. 11714-11740. ISSN 1050-6926. doi:10.1007/s12220-021-00699-w. https://resolver.caltech.edu/CaltechAUTHORS:20210608-103915433

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Abstract

Let f be a harmonic map from a Riemann surface to a Riemannian n-manifold. We prove that if there is a holomorphic diffeomorphism h between open subsets of the surface such that f∘h=f, then f factors through a holomorphic map onto another Riemann surface. If such h is anti-holomorphic, we obtain an analogous statement. For minimal maps, this result is well known and is a consequence of the theory of branched immersions of surfaces due to Gulliver–Osserman–Royden. Our proof relies on various geometric properties of the Hopf differential.


Item Type:Article
Related URLs:
URLURL TypeDescription
https://doi.org/10.1007/s12220-021-00699-wDOIArticle
https://rdcu.be/cmaeqPublisherFree ReadCube access
https://arxiv.org/abs/2009.08377arXivDiscussion Paper
ORCID:
AuthorORCID
Sagman, Nathaniel0000-0002-8485-7073
Additional Information:© Mathematica Josephina, Inc. 2021. Received 25 November 2020; Accepted 09 May 2021; Published 24 May 2021. Many thanks to Vlad Markovic for encouragement and sharing helpful ideas. I would also like to thank John Wood and Jürgen Jost for comments on earlier drafts.
Subject Keywords:Harmonic map; Minimal surface; Riemann surface; Klein surface; Hopf differential
Issue or Number:12
Classification Code:Mathematics Subject Classification: 58E20; 53A10; 14H55; 30F50
DOI:10.1007/s12220-021-00699-w
Record Number:CaltechAUTHORS:20210608-103915433
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20210608-103915433
Official Citation:Sagman, N. A Factorization Theorem for Harmonic Maps. J Geom Anal 31, 11714–11740 (2021). https://doi.org/10.1007/s12220-021-00699-w
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:109441
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:09 Jun 2021 18:31
Last Modified:13 Oct 2021 15:59

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