On the uniqueness of vortex equations and its geometric applications

2017/10/30 by Li, Qiongling · 2 citations
#53C21 #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1710.10729

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→ 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 finite zeros.

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