The double and triple bubble problem for stationary varifolds: the convex case

TL;DR

This paper characterizes the critical points of double and triple bubble problems in convex settings, providing insights into their geometric configurations in Euclidean spaces.

Contribution

It offers a new characterization of critical points for convex double and triple bubble problems in Euclidean spaces, advancing understanding in geometric measure theory.

Findings

Identifies critical points for convex double bubbles in any dimension.

Characterizes critical points for convex triple bubbles in three dimensions.

Provides geometric conditions for optimal bubble configurations.

Abstract

We characterize the critical points of the double bubble problem in $\mathbb{R}^n$ and the triple bubble problem in $\mathbb{R}^3$, in the case the bubbles are convex.