An Elementary Proof for the Double Bubble Problem in ℓ1 Norm

Parker Duncan; Rory O’Dwyer; Eviatar B. Procaccia

doi:https://doi.org/10.1007/s12220-022-01008-9

An Elementary Proof for the Double Bubble Problem in ℓ¹ Norm

Parker Duncan, Rory O’Dwyer, Eviatar B. Procaccia

Data and Decision Sciences

Technion - Israel Institute of Technology

Research output: Contribution to journal › Article › peer-review

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 < α≤ 1 by direct comparison to a small family of parameterized sets. By simple analysis on this family, we obtain the minimizing shapes found in Morgan et al. in J Geom Anal 8(1):97-*115 , 1998.

Original language	English
Article number	31
Journal	Journal of Geometric Analysis
Volume	33
Issue number	1
DOIs	https://doi.org/10.1007/s12220-022-01008-9
State	Published - Jan 2023

Keywords

Double bubble problem
Isoperimetry
Optimization
Taxicab metric

All Science Journal Classification (ASJC) codes

Geometry and Topology

Access to Document

https://doi.org/10.1007/s12220-022-01008-9

Cite this

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