2024/01/18 by Parker Duncan, Duncan, Parker, Rory O’Dwyer +3
Computer Science · Mathematics · #Computational Geometry and Mesh Generation #Digital Image Processing Techniques #FOS: Mathematics #Geometric Topology (math.GT) #Metric Geometry (math.MG) #Point processes and geometric inequalities
paper · pdf · doi:10.48550/arxiv.2401.09893
openalex publication_date 2024/01/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study the double bubble problem where the perimeter is taken with respect to the hexagonal norm, i.e. the norm whose unit circle in ℝ2 is the regular hexagon. We provide an elementary proof for the existence of minimizing sets for volume ratio parameter α∈ (0,1] by arguing that any minimizer must belong to a small family of parameterized sets. This family is further simplified by showing that 60∘ angles are not optimal as well as other geometric exclusions. We then provide a minimizer for all α∈(0,1] except at a single point, for which we find two minimizing configurations.