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

Abstract

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

15 pages 14 figures