Colloquium: Tuesday April 21. Speaker: Daoud Bshouty . Title: Univalent Harmonic Mappings onto Polygons.
Tuesday April 21 at 2 pm in room 614.
Speaker: Daoud Bshouty (Technion)
Title: Univalent Harmonic Mappings onto Polygons.
Abstract: A sense preserving harmonic mapping as opposed to analytic mapping is a function f=u+iv from a domain in the complex plane to the complex plane where u and v are real harmonic function with positive Jacobian but otherwise unrelated. Jenkins and Serrin characterized all polygons on which there exists a nonparametric minimal surface above them with boundary values plus or minus infinity. We show that on every polygon there exist infinitely many parametric minimal surfaces.