Morse-Rad\'o Theory for Minimal Surfaces

TL;DR

This paper introduces bounds on the interior critical points of minimal Rado functions, linking their count to boundary data and domain topology, advancing understanding in minimal surface theory.

Contribution

It provides new bounds on interior critical points for minimal Rado functions, connecting critical point counts with boundary conditions and Euler characteristic.

Findings

Bound on interior critical points in terms of boundary data

Relation between critical points and Euler characteristic

Advancement in minimal surface theory understanding

Abstract

For a class of functions (called minimal Rad\'o functions) that arise naturally in minimal surface theory, we bound the number of interior critical points (counting multiplicity) in terms of the boundary data and the Euler characteristic of the domain of the function.