Isoperimetric 3- and 4-Bubble Results on R With Density |x|
Keywords:
isoperimetric problem; density; geometric optimization
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.
Published
2023-06-01
How to Cite
Alexander, E., Burns, E., Ross, J., Stovall, J., & Whyte, Z. (2023). Isoperimetric 3- and 4-Bubble Results on R With Density |x|. The PUMP Journal of Undergraduate Research, 6, 192-223. Retrieved from https://journals.calstate.edu/pump/article/view/3618
Section
Articles
Copyright (c) 2023 Evan Alexander, Emily Burns, John Ross, Jesse Stovall, Zariah Whyte

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