On branch points and C^{1,1} pseudospherical immersions

Abstract: This is a report of joint work with Toby Shearman. The key result is that one can define a (local) winding number of the Gauss Map for $C^{1,1}$ hyperbolic surfaces in $R^3$ and this degree is an obstruction for approximation by smooth immersions in $W^{2,2}_{loc}$. I will discuss the ideas behind the proof, as well as the motivation for studying this question, which comes from the mechanics of non-Euclidean plates.

mathematical physicsanalysis of PDEsclassical analysis and ODEsdifferential geometryfunctional analysismetric geometrynumerical analysisoptimization and control

Audience: researchers in the topic

Online Seminar "Geometric Analysis"

Series comments: We discuss recent trends related to geometric analysis in a broad sense. The general idea is to solve geometric problems by means of advanced tools in analysis. We will include a wide range of topics such as geometric flows, curvature functionals, discrete differential geometry, and numerical simulation.

Registration and links to videos available at blatt.sbg.ac.at/onlineseminar.php