Existence of Embedded Minimal Disks

TL;DR

This paper generalizes a key result on the embeddedness of minimal disks, extending the classical theorem to broader classes of solutions for the Plateau problem involving extreme curves.

Contribution

It introduces a new generalized theorem ensuring embeddedness of minimal disks for a wider range of boundary conditions compared to previous results.

Findings

Established a generalized embeddedness theorem for minimal disks.

Extended classical results to extreme curves in the Plateau problem.

Provided new insights into the structure of solutions for minimal surface equations.

Abstract

We give a generalization of Meeks-Yau's celebrated embeddedness result for the solutions of the Plateau problem for extreme curves.