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
收藏
页码：105 / 120
页数：16
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