The planar soap bubble problem with equal pressure regions

Banyat Sroysang, Wacharin Wichiramala

Abstract

The planar soap bubble problem seeks the least-perimeter way to enclose and separate regions of m given areas in $R^2$. We study the possible configurations for perimeter minimizing enclosures for more than three regions. For four and five regions, we prove that a perimeter minimizing enclosure with equal pressure regions must have connected.