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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
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Abstract |
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We prove the double bubble conjecture in : that the standard double bubble in 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
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Mathematical Subject Classification 2000
Primary: 49Q05, 49Q10, 53A10
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Milestones
Received: 22 October 2009
Accepted: 23 October 2009
Published: 13 January 2010
Communicated by Frank Morgan
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Authors |
| Rebecca Dorff | |
| Mathematics Department Brigham Young University Provo, UT 84602 United States |
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| Gary Lawlor | |
| Department of Mathematics
Education Brigham Young University 185 TMCB Provo, UT 84602 United States |
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| Donald Sampson | |
| Mathematics Department Brigham Young University Provo, UT 84602 United States |
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| http://sites.google.com/site/sampsondcs/ | |
| Brandon Wilson | |
| Mathematics Department Duke University Box 90320 Durham, NC 27708-0320 United States |
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