Geometry & Topology Seminar: On the uniqueness of the coupled vortex equation

Monday, April 24 at 4:30pm to 5:30pm

Kaprielian Hall (KAP), 245
3620 South Vermont Avenue, Los Angeles, CA 90089

Qionling Li, Caltech

Abstract:
We study the uniqueness of a coupled vortex equation involving a holomorphic k-differential on the complex plane. As geometric applications, we show that there is a unique non-branching harmonic map from the complex plane into the hyperbolic 2-space with prescribed polynomial Hopf differential; there is a unique affine spherical immersion from the complex plane into the Euclidean 3-space with prescribed polynomial Pick differential. We also show that the uniqueness always fails for non-polynomial k-differentials with finite zeros.

Event Type

Lecture / Talk / Workshop

Campus

University Park Campus

Department

Mathematics

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