Monday, April 24 at 4:30pm to 5:30pm
Kaprielian Hall (KAP), 245
3620 South Vermont Avenue, Los Angeles, CA 90089
Qionling Li, Caltech
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.