We consider the soap bubble problem on the sphere S2, which seeks a perimeter-minimizing partition into n regions of given areas. For n = 4, it is conjectured that a tetrahedral partition is minimizing. We prove that there exists a unique tetrahedral partition into given areas, and that this partition has less perimeter than any other partition dividing the sphere into the same four connected areas.
Frank Morgan, Department of Mathematics, Williams College Frank.Morgan@williams.edu
"Minimal connected partitions of the sphere,"
Rose-Hulman Undergraduate Mathematics Journal: Vol. 11
, Article 1.
Available at: http://scholar.rose-hulman.edu/rhumj/vol11/iss2/1