Minimal connected partitions of the sphere
نویسنده
چکیده
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. Page 2 RHIT Undergrad. Math. J., Vol. 11, No. 2
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