Published January 2019
| Published + Submitted
Journal Article
Open
On the Uniqueness of Vortex Equations and Its Geometric Applications
- Creators
- Li, Qiongling
Abstract
We study the uniqueness of a vortex equation involving an entire function on the complex plane. As geometric applications, we show that there is a unique harmonic map u : C → H^2 satisfying ∂u ≠ 0 with prescribed polynomial Hopf differential; there is a unique affine spherical immersion u : C → R^3 with prescribed polynomial Pick differential. We also show that the uniqueness fails for non-polynomial entire functions with finitely many zeros.
Additional Information
© 2018 Mathematica Josephina, Inc. Received 02 October 2017; First Online 12 January 2018. The author wishes to thank Vlad Markovic, Song Dai and Mike Wolf for helpful discussions. The author is supported by the center of excellence grant 'Center for Quantum Geometry of Moduli Spaces' from the Danish National Research Foundation (DNRF95). She also acknowledges the support from U.S. National Science Foundation Grants DMS 1107452, 1107263, 1107367 "RNMS: GEometric structures And Representation varieties" (the GEAR Network).Attached Files
Published - Li2019_Article_OnTheUniquenessOfVortexEquatio.pdf
Submitted - 1710.10729.pdf
Files
1710.10729.pdf
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Additional details
- Eprint ID
- 92438
- Resolver ID
- CaltechAUTHORS:20190124-070333680
- DNRF95
- Danish National Research Foundation
- DMS-1107452
- NSF
- DMS-1107263
- NSF
- DMS-1107367
- NSF
- Created
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2019-01-24Created from EPrint's datestamp field
- Updated
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2021-11-16Created from EPrint's last_modified field