The sharp diameter bound of stable minimal surfaces

TL;DR

This paper establishes the precise maximum diameter for complete stable minimal surfaces within three-dimensional Riemannian manifolds that have scalar curvature at least one.

Contribution

It provides the first sharp upper bound on the diameter of stable minimal surfaces under scalar curvature constraints in three dimensions.

Findings

Sharp diameter bound proven for stable minimal surfaces

Bound applies to manifolds with scalar curvature ≥ 1

Results improve understanding of geometric constraints on minimal surfaces

Abstract

For three dimensional complete Riemannian manifolds with scalar curvature no less than one, we obtain the sharp upper bound of complete stable minimal surfaces' diameter.