H\"older regularity at the boundary of two-dimensional sliding almost minimal sets

TL;DR

This paper establishes boundary regularity results for two-dimensional sliding almost minimal sets in three-dimensional space, enhancing understanding of their boundary behavior relevant to soap films and Plateau's problem.

Contribution

It extends regularity theory to boundary points for sliding almost minimal sets, a significant advancement over previous interior regularity results.

Findings

Proves boundary regularity for sliding almost minimal sets in b2b0b0 space

Provides tools for analyzing boundary behavior of soap films

Enhances understanding of Plateau's problem solutions near boundary

Abstract

In [15], Jean Taylor has proved a regularity theorem away from boundary for Almgren almost minimal sets of dimension two in $\mathbb{R}^{3}$. It is quite important for understanding the soap films and the solutions of Plateau's problem away from boundary. In this paper, we will give a regularity result on the boundary for two dimensional sliding almost minimal sets in $\mathbb{R}^{3}$. It will be of use for understanding their boundary behavior.