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 ${ℝ}^{2}$: that the standard double bubble in ${ℝ}^{2}$ 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