1998/08/11 by Rick Vaughn, Vaughn, Rick
Mathematics · #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #Metric Geometry (math.MG) #Point processes and geometric inequalities #math.DG #math.MG
paper · pdf · doi:10.48550/arxiv.math/9808051
arxiv created 1998/08/11 · openalex publication_date 1998/08/11 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The generalized soap bubble problem seeks the least perimeter way to enclose and separate n given volumes in Rm. We study the possible configurations for perimeter minimizing bubble complexes enclosing more than two regions. We prove that perimeter minimizing planar bubble complexes with equal pressure regions and without empty chambers must have connected regions. As a consequence, we show that the least perimeter planar graph that encloses and separates three equal areas in R2 using convex cells and without empty chambers is a "standard triple bubble" with connected regions.