The Least-Perimeter Partition of a Sphere into Four Equal Areas

2009/03/24 by Max Engelstein, Engelstein, Max
Mathematics · #53C42 #Differential Geometry (math.DG) #FOS: Mathematics #math.DG #msc:53C42

paper · pdf · doi:10.48550/arxiv.0903.4097

7 pages, 1 figure, PDFLaTeX. Minor cosmetic/typo revisions. Accepted to the Journal of Discrete and Computational Geometry

arxiv created 2009/06/19 · arxiv updated 2009/12/01

Abstract

We prove that the least-perimeter partition of the sphere into four regions of equal area is a tetrahedral partition.

Related

• The Honeycomb Problem on the Sphere
• Planar Clusters
• A property of the bidimensional sphere
• Least-perimeter partitions of the disk into three regions of given areas
• Compact packings of space with three sizes of spheres