Chord arc properties for constant mean curvature disks

Abstract

We prove a chord arc bound for disks embedded in ${\mathbb{R}}^3$ with constant mean curvature. This bound does not depend on the value of the mean curvature. It is inspired by and generalizes the work of Colding and Minicozzi in [2] for embedded minimal disks. Like in the minimal case, this chord arc bound is a fundamental tool for studying complete constant mean curvature surfaces embedded in ${\mathbb{R}}^3$ with finite topology or with positive injectivity radius.

Details added at referee's request. To appear in Geometry & Topology

References in corpus (3)

• General curvature estimates for stable H-surfaces in 3-manifolds and applications
• Curvature estimates for constant mean curvature surfaces
• The geometry of constant mean curvature surfaces in ${\mathbb{R}}^3$

Cited by in corpus (1)

• Curvature estimates for constant mean curvature surfaces