Isoperimetric 3- and 4-bubble results on ℝ with density |x|

2022/01/05 by Evan Alexander, Alexander, Evan, Emily Burns +7
Computer Science · Mathematics · #49Q10 #Advanced Mathematical Modeling in Engineering #FOS: Mathematics #Mathematical Approximation and Integration #Metric Geometry (math.MG) #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.2201.02197

openalex publication_date 2022/01/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study the isoperimetric problem on ℝ¹ with a prescribed density function f(x) = |x|. Under these conditions, we find that isoperimetric 3-bubble and 4-bubble results satisfy a regular structure. As our regions increase in size, the intervals that form them alternate back-and-forth across the origin, with the smaller regions closer to the origin. This expands on previously known observations about the single- and double-bubble results on ℝ with density |x|^p.

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