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Chord arc properties for
constant mean curvature disks
William H Meeks, III and Giuseppe Tinaglia |
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Geometry & Topology 22 (2018) 305–322
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Abstract |
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We prove a chord arc type bound for disks embedded in 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 with finite topology or with positive injectivity radius. |
Keywords
minimal surface, constant mean curvature, minimal
lamination, positive injectivity radius, curvature
estimates, one-sided curvature estimate, chord arc
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Mathematical Subject Classification 2010
Primary: 53A10
Secondary: 49Q05, 53C42
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References |
Publication
Received: 4 November 2015
Revised: 12 March 2017
Accepted: 9 April 2017
Published: 31 October 2017
Proposed: Tobias H. Colding
Seconded: Bruce Kleiner, Gang Tian
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Authors |
| William H Meeks, III | |
| Department of Mathematics University of Massachusetts Amherst, MA United States |
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| Giuseppe Tinaglia | |
| Department of Mathematics King’s College London London United Kingdom |
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