The planar soap bubble problem with equal pressure regions
Banyat Sroysang, Wacharin Wichiramala · Thai Journal of Mathematics · 2012
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.