Chord arc properties for constant mean curvature disks

2014/08/31 by William H. Meeks III, Giuseppe Tinaglia
Mathematics · #math.DG #msc:53A10

paper · pdf · doi:10.2140/gt.2018.22.305

published as Geom. Topol. 22 (2018) 305-322 · Details added at referee's request. To appear in Geometry & Topology

arxiv created 2017/04/10 · arxiv updated 2018/03/16

Abstract

We prove a chord arc bound for disks embedded in ℝ³ 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 ℝ³ with finite topology or with positive injectivity radius.

Cited by

• Calabi-Yau Conjecture for Minimal Hypersurfaces in ℝ⁴ with bounded geometry