Conjecture on least-perimeter partitions of the disk into six regions

Let the unit disk be divided into six regions with prescribed areas. A minimizing partition is a partition whose total perimeter is least among all such divisions.

Least-perimeter six-region partition conjecture. The least-perimeter way of dividing the unit disk into six regions of prescribed areas is given by the configuration shown in Figure~.

This conjecture concerns the extension of the least-perimeter partition problem from three, four, and five regions to six regions. The referenced configuration is not described in the supplied text, and the conjecture's status is not established here.