Helicoid-Like Minimal Disks and Uniqueness

TL;DR

This paper demonstrates that embedded minimal disks with large curvature resemble a helicoid and offers a simplified proof of the helicoid's uniqueness in minimal surface theory.

Contribution

It establishes a bilipschitz equivalence between large curvature minimal disks and helicoids and simplifies the proof of the helicoid's uniqueness.

Findings

Embedded minimal disks with large curvature are bilipschitz to a helicoid.

Provides a simplified proof of the helicoid's uniqueness.

Enhances understanding of minimal surface geometry.

Abstract

We show that an embedded minimal disk in R^3 with large curvature is bilipschitz with a piece of a helicoid. Additionally, a simplified proof of the uniqueness of the helicoid is provided.