Chord arc properties for constant mean curvature disks

TY - JOUR

T1 - Chord arc properties for constant mean curvature disks

AU - H. Meeks III, William

AU - Tinaglia, Giuseppe

PY - 2017

Y1 - 2017

N2 - We prove a chord arc type bound for disks embedded in R3 with constant mean curvature that does not depend on the value of the mean curvature. This bound is inspired by and generalizes the weak chord arc bound of Colding and Minicozzi in Proposition 2.1 of Ann. of Math. 167 (2008) 211–243 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.

AB - We prove a chord arc type bound for disks embedded in R3 with constant mean curvature that does not depend on the value of the mean curvature. This bound is inspired by and generalizes the weak chord arc bound of Colding and Minicozzi in Proposition 2.1 of Ann. of Math. 167 (2008) 211–243 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.

U2 - 10.2140/gt.2018.22.305

DO - 10.2140/gt.2018.22.305

M3 - Article

SN - 1465-3060

VL - 22

SP - 305

EP - 322

JO - Geometry & Topology

JF - Geometry & Topology

ER -