Local minimizers of the area functional based on a concept of local paired calibrations

Abstract: Calibrations are an elegant tool to prove that a given surface (or surface cluster) minimizes the area functional. In this talk, I will present a way to extend the notion of (paired) calibrations to the setting when one can only hope for local minimality. Based on this notion, one can show that any partition of the plane, whose network of interfaces consists of finitely many straight segments with a singular set made up of finitely many triple junctions at which the Herring angle condition is satisfied, is a local minimizer of the interface energy with respect to $L^1$ perturbations of the phases. This result not only holds for the case of the area functional but for a general class of surface tension matrices.

This is based on joint work with Julian Fischer, Sebastian Hensel, and Theresa Simon.

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