1D Triple Bubble Problem with Log-Convex Density

TL;DR

This paper classifies the types of perimeter-minimizing triple bubbles on the real line with symmetric, strictly log-convex densities, extending previous double bubble results to triple bubbles.

Contribution

It establishes that four types of perimeter-minimizing triple bubbles exist under symmetric, strictly log-convex densities, expanding the understanding from double to triple bubble configurations.

Findings

Four possible types of perimeter-minimizing triple bubbles identified.

Extension of double bubble results to triple bubbles.

Provides a classification framework for bubble minimization problems.

Abstract

We prove that for a symmetric, strictly log-convex density on the real line, there are four possible types of perimeter-minimizing triple bubbles. This extends the work of Bongiovanni et al., which shows that there are two possible types of perimeter-minimizing double bubbles.