Sharp stability inequalities for planar double bubbles

TL;DR

This paper establishes sharp stability inequalities for planar double bubbles, combining advanced convergence theorems with specialized analysis to understand the stability and singularity interactions under volume constraints.

Contribution

It introduces new stability inequalities for planar double bubbles by integrating improved convergence results with detailed analysis of singularity dislocation.

Findings

Proves sharp stability inequalities for planar double bubbles

Analyzes the interaction between singularities and volume constraints

Extends understanding of stability in geometric cluster problems

Abstract

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.