An elementary proof for the Double Bubble problem in ℓ¹ norm

2020/08/18 by Parker Duncan, Duncan, Parker, Rory O’Dwyer +3 · 1 citation
Engineering · Materials Science · Mathematics · #Enhanced Oil Recovery Techniques #FOS: Mathematics #Geometric Topology (math.GT) #Pickering emulsions and particle stabilization #Point processes and geometric inequalities

paper · pdf · doi:10.48550/arxiv.2008.07767

openalex publication_date 2020/08/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study the double bubble problem with perimeter taken with respect to the ℓ₁ norm on ℝ². We give an elementary proof for the existence of minimizing sets for any volume ratio parameter 0

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