On the uniqueness of vortex equations and its geometric applications

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On the uniqueness of vortex equations and its geometric applications. / Li, Qiongling.

In: Journal of Geometric Analysis, Vol. 29, No. 1, 01.2019, p. 105-120.

Research output: Contribution to journal/Conference contribution in journal/Contribution to newspaperJournal articleResearchpeer-review

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Li, Q 2019, 'On the uniqueness of vortex equations and its geometric applications', Journal of Geometric Analysis, vol. 29, no. 1, pp. 105-120. https://doi.org/10.1007/s12220-018-9981-x

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Author

Li, Qiongling. / On the uniqueness of vortex equations and its geometric applications. In: Journal of Geometric Analysis. 2019 ; Vol. 29, No. 1. pp. 105-120.

Bibtex

@article{93de7672067145fe828579e0c5bdee03,
title = "On the uniqueness of vortex equations and its geometric applications",
abstract = "We study the uniqueness of a vortex equation involving an entire function onthe complex plane. As geometric applications, we show that there is a unique harmonic map u : C → H2 satisfying ∂u = 0 with prescribed polynomial Hopf differential; there is a unique affine spherical immersion u : C → R3 with prescribed polynomial Pick differential. We also show that the uniqueness fails for non-polynomial entire functions with finitely many zeros.",
keywords = "Harmonic maps, Polynomial differentials, Vortex equations, CUBIC DIFFERENTIALS, HARMONIC MAPS, SURFACE, CALABI CONJECTURE",
author = "Qiongling Li",
year = "2019",
month = "1",
doi = "10.1007/s12220-018-9981-x",
language = "English",
volume = "29",
pages = "105--120",
journal = "Journal of Geometric Analysis",
issn = "1050-6926",
publisher = "Springer New York LLC",
number = "1",

}

RIS

TY - JOUR

T1 - On the uniqueness of vortex equations and its geometric applications

AU - Li, Qiongling

PY - 2019/1

Y1 - 2019/1

N2 - We study the uniqueness of a vortex equation involving an entire function onthe complex plane. As geometric applications, we show that there is a unique harmonic map u : C → H2 satisfying ∂u = 0 with prescribed polynomial Hopf differential; there is a unique affine spherical immersion u : C → R3 with prescribed polynomial Pick differential. We also show that the uniqueness fails for non-polynomial entire functions with finitely many zeros.

AB - We study the uniqueness of a vortex equation involving an entire function onthe complex plane. As geometric applications, we show that there is a unique harmonic map u : C → H2 satisfying ∂u = 0 with prescribed polynomial Hopf differential; there is a unique affine spherical immersion u : C → R3 with prescribed polynomial Pick differential. We also show that the uniqueness fails for non-polynomial entire functions with finitely many zeros.

KW - Harmonic maps

KW - Polynomial differentials

KW - Vortex equations

KW - CUBIC DIFFERENTIALS

KW - HARMONIC MAPS

KW - SURFACE

KW - CALABI CONJECTURE

U2 - 10.1007/s12220-018-9981-x

DO - 10.1007/s12220-018-9981-x

M3 - Journal article

VL - 29

SP - 105

EP - 120

JO - Journal of Geometric Analysis

JF - Journal of Geometric Analysis

SN - 1050-6926

IS - 1

ER -