Chord arc properties for constant mean curvature disks

William Meeks, Giuseppe Tinaglia
2017 Geometry and Topology  
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.
doi:10.2140/gt.2018.22.305 fatcat:5an6hnlamja4pen7numtkzoyte