King's College London

Research portal

Chord arc properties for constant mean curvature disks

Research output: Contribution to journalArticle

William H. Meeks III, Giuseppe Tinaglia

Original languageEnglish
Pages (from-to)305-322
JournalGeometry & Topology
Early online date20 Dec 2017
Accepted/In press9 Apr 2017
E-pub ahead of print20 Dec 2017


King's Authors


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.

Download statistics

No data available

View graph of relations

© 2020 King's College London | Strand | London WC2R 2LS | England | United Kingdom | Tel +44 (0)20 7836 5454