Inserted: 5 nov 2012
Last Updated: 20 apr 2015
In this paper we address the global stability problem for double-bubbles in the plane. This is accomplished by combining the improved convergence theorem for planar clusters we have developed in "Improved convergence theorems for bubble clusters. I. The planar case" with an ad hoc analysis of the problem, which addresses the delicate interaction between the (possible) dislocation of singularities and the multiple-volumes constraint.