Isoperimetric 3- and 4-Bubble Results on R With Density |x|

Authors

  • Evan Alexander Southwestern University
  • Emily Burns Southwestern University
  • John Ross Southwestern University
  • Jesse Stovall Southwestern University
  • Zariah Whyte Southwestern University

DOI:

https://doi.org/10.46787/pump.v6i0.3618

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.

Downloads

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. https://doi.org/10.46787/pump.v6i0.3618