Least-perimeter partitions of the disk into three regions of given areas

2003/07/15 by Antonio Cañete, Cañete, Antonio, Manuel Ritoré +1
Engineering · Mathematics · #49Q10 (Primary) 51M25 (Secondary) #Advanced Numerical Analysis Techniques #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Point processes and geometric inequalities #math.DG #msc:49Q10 #msc:51M25

paper · pdf · doi:10.48550/arxiv.math/0307207

19 pages, 8 figures

arxiv created 2003/07/15 · openalex publication_date 2003/07/15 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove that the unique least-perimeter way of partitioning the unit 2-dimensional disk into three regions of prescribed areas is by means of the standard graph consisting in three balanced constant geodesic curvature curves meeting themselves at 120 degrees, and reaching orthogonally the boundary of the disk.

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