Numerically computed Double, Triple, and Quadruple Planar Bubbles for Density $r^p$

TL;DR

This paper uses numerical methods to verify and conjecture optimal configurations of double, triple, and quadruple planar bubbles under a specific density function, advancing understanding of minimal surface partitions.

Contribution

It provides the first numerical verification of conjectured optimal double bubbles and introduces new conjectures for triple and quadruple bubbles under density $r^p$.

Findings

Numerical verification of optimal double bubbles for density $r^p$

Conjectures for optimal triple and quadruple bubbles

Use of Brakke's Evolver for surface energy minimization

Abstract

Using Brakke's Evolver, we numerically verify conjectured optimal planar double bubbles for density $r^p$ and provide conjectures for triple and quadruple bubbles.