On the uniqueness of vortex equations and its geometric applications

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  • Qiongling Li, California Institute of Technology
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 finitely many zeros.
Original languageEnglish
JournalJournal of Geometric Analysis
Pages (from-to)105-120
Number of pages16
Publication statusPublished - Jan 2019

    Research areas

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

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