Curvature estimates for constant mean curvature surfaces

TL;DR

This paper establishes extrinsic curvature bounds for compact constant mean curvature surfaces embedded in three-dimensional space, providing new geometric estimates for such surfaces.

Contribution

It introduces novel extrinsic curvature estimates specifically for compact disks with nonzero constant mean curvature in 3.

Findings

Derived explicit curvature bounds for CMC surfaces

Extended understanding of geometric properties of CMC surfaces

Provided tools for analyzing embedded CMC surfaces

Abstract

We derive extrinsic curvature estimates for compact disks embedded in $\mathbb{R}^3$ with nonzero constant mean curvature.