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.

Author Bio

After attending Williams College as an undergraduate - where the work described in this paper served as his senior thesis - Edward Newkirk is now working towards a PhD at Brown University. A childhood in England left him with permanent fondness for soccer (particularly Chelsea F.C) and various British science fiction authors.