Vol. 2, No. 5, 2009

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Proof of the planar double bubble conjecture using metacalibration methods

Rebecca Dorff, Gary Lawlor, Donald Sampson and Brandon Wilson

Vol. 2 (2009), No. 5, 611–628
Abstract

We prove the double bubble conjecture in 2: that the standard double bubble in 2 is boundary length-minimizing among all figures that separately enclose the same areas. Our independent proof is given using the new method of metacalibration, a generalization of traditional calibration methods useful in minimization problems with fixed volume constraints.

Keywords
calibration, metacalibration, double bubble, isoperimetric, optimization
Mathematical Subject Classification 2000
Primary: 49Q05, 49Q10, 53A10
Milestones
Received: 22 October 2009
Accepted: 23 October 2009
Published: 13 January 2010

Communicated by Frank Morgan
Authors
Rebecca Dorff
Mathematics Department
Brigham Young University
Provo, UT 84602
United States
Gary Lawlor
Department of Mathematics Education
Brigham Young University
185 TMCB
Provo, UT 84602
United States
Donald Sampson
Mathematics Department
Brigham Young University
Provo, UT 84602
United States
http://sites.google.com/site/sampsondcs/
Brandon Wilson
Mathematics Department
Duke University
Box 90320
Durham, NC 27708-0320
United States