Proof of the planar double bubble conjecture using metacalibration methods

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.