Sharp stability inequalities for planar double bubbles
  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 developed in arXiv:1409.6652 with an ad hoc analysis of the problem, which addresses the delicate interaction between the (possible) dislocation of singularities and the multiple-volumes constraint. 
Marco Cicalese, Gian Paolo Leonardi, Francesco Maggi
math.AP