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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
Volume22
Early online date20 Dec 2017
DOIs
Accepted/In press9 Apr 2017
E-pub ahead of print20 Dec 2017
Published2017

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Abstract

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.

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