PDE Seminar Abstracts

The two-valued minimal surface equation

Leobardo Rosales
Rice University, Houston, USA
1 Mar 2010 3-4pm, Carslaw Room 273

Abstract

We discuss a PDE method for producing examples of immersed minimal surfaces in the unit cylinder in ${ℝ}^{3},$ as graphs of two-valued functions over the punctured unit disk. These two-valued functions can either be extended continuously across the origin, in which case the two-valued graph is a stable branched minimal immersion, or we can give an asymptotic description of the graphs near the vertical axis. Various analogies to the theory of the Minimal Surface Equation will be illustrated.