Area minimizing surfaces for singular boundary values

Paul Creutz (University of Cologne)

02-Feb-2021, 18:00-19:00 (3 years ago)

Abstract: Fix a nonnegative integer g and a finite configuration of disjoint Jordan curves in Euclidean space. Then, by a classical result of Douglas, there is an area minimizer among all surfaces of genus at most g which span the given curve configuration. In the talk I will discuss a generalization of this theorem to singular configurations of possibly non-disjoint or self-intersecting curves. The proof relies on an existence result for minimal surfaces in singular metric spaces and does not seem amenable within classical smooth techniques.

This is joint work with M. Fitzi.

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

Organizers: Simon Blatt*, Philipp Reiter*, Armin Schikorra*, Guofang Wang
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