Published December 2021
| Submitted
Journal Article
Open
A Factorization Theorem for Harmonic Maps
- Creators
- Sagman, Nathaniel
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.
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.Attached Files
Submitted - 2009.08377.pdf
Files
2009.08377.pdf
Files
(285.9 kB)
Name | Size | Download all |
---|---|---|
md5:96c9cdb4a62ac13102d7ffeb6aa55750
|
285.9 kB | Preview Download |
Additional details
- Eprint ID
- 109441
- Resolver ID
- CaltechAUTHORS:20210608-103915433
- Created
-
2021-06-09Created from EPrint's datestamp field
- Updated
-
2021-10-13Created from EPrint's last_modified field