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Discrete \(\ell ^{1}\) Double Bubble Solution is at Most Ceiling Plus Two of the Continuous Solution

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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 Morgan et al. (J. Geom. Anal. 8(1), 97–115 (1998)) and Duncan et al. (J. Geom. Anal. 33(1), # 31 (2023)).

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Authors and Affiliations

  1. Faculty of Data and Decision Sciences, Technion - Israel Institute of Technology, Haifa, Israel

    Parker Duncan & Eviatar B. Procaccia

  2. Department of Mathematics, Texas A &M University, College Station, USA

    Parker Duncan

  3. Department of Physics, Stanford University, Stanford, USA

    Rory O’Dwyer

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  1. Parker Duncan
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  2. Rory O’Dwyer
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  3. Eviatar B. Procaccia
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Correspondence to Rory O’Dwyer.

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Eviatar B. Procaccia: Research partially supported by NSF Grant 1812009 and BSF Grant 2018330.

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Duncan, P., O’Dwyer, R. & Procaccia, E.B. Discrete \(\ell ^{1}\) Double Bubble Solution is at Most Ceiling Plus Two of the Continuous Solution. Discrete Comput Geom 71, 688–707 (2024). https://doi.org/10.1007/s00454-023-00501-4

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  • DOI: https://doi.org/10.1007/s00454-023-00501-4

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