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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