On the Uniqueness of Vortex Equations and Its Geometric Applications

被引：9

作者：

Li, Qiongling ^{[1
,2
]}

机构：

[1] Aarhus Univ, Ctr Quantum Geometry Moduli Spaces QGM, Ny Munkegade 118, DK-8000 Aarhus C, Denmark

[2] CALTECH, Dept Math, 1200 East Calif Blvd, Pasadena, CA 91125 USA

来源：

JOURNAL OF GEOMETRIC ANALYSIS | 2019年 / 29卷 / 01期

基金：

美国国家科学基金会; 新加坡国家研究基金会;

关键词：

Vortex equations; Polynomial differentials; Harmonic maps; HARMONIC MAPS; CUBIC DIFFERENTIALS; CALABI CONJECTURE; SURFACE;

D O I：

10.1007/s12220-018-9981-x

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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:CH2 satisfying u0 with prescribed polynomial Hopf differential; there is a unique affine spherical immersion u:CR3 with prescribed polynomial Pick differential. We also show that the uniqueness fails for non-polynomial entire functions with finitely many zeros.

引用

页码：105 / 120

页数：16

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