English

Discrete $\ell^{1}$ Double Bubble solution is at most ceiling +2 of the continuous solution

Metric Geometry 2021-09-27 v1 Probability

Abstract

In this paper we show that the solution of the discrete Double Bubble problem over Z2\mathbb{Z}^2 is at most the ceiling function plus two of the continuous solution to the Double Bubble problem, with respect to the 1\ell^1 norm, found in \cite{morgan1998wulff} and \cite{duncan2020elementary}.

Cite

@article{arxiv.2109.11879,
  title  = {Discrete $\ell^{1}$ Double Bubble solution is at most ceiling +2 of the continuous solution},
  author = {Parker Duncan and Rory O'Dwyer and Eviatar B. Procaccia},
  journal= {arXiv preprint arXiv:2109.11879},
  year   = {2021}
}

Comments

15 pages 14 figures

R2 v1 2026-06-24T06:17:32.928Z