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The Local Optimality of the Double Lattice Packing

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Abstract

This paper introduces a new technique for proving the local optimality of packing configurations of Euclidean space. Applying this technique to a general convex polygon, we prove that under mild assumptions satisfied generically, the construction of the optimal double lattice packing by Kuperberg and Kuperberg is also locally optimal in the full space of packings.

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Acknowledgments

Y. K. was supported by an Omidyar Fellowship at the Santa Fe Institute. W. K. was supported by Austrian Science Fund (FWF) Project 5503 and National Science Foundation (NSF) Grant No. 1104102. We wish to thank the Erwin Schrödinger International Institute for Mathematical Physics (ESI) and the Institute for Computational and Experimental Research (ICERM) for supporting our visits and hosting programs that facilitated this work.

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Authors and Affiliations

  1. Santa Fe Institute, 1399 Hyde Park Road, Santa Fe, NM, USA

    Yoav Kallus

  2. Institute of Analysis and Number Theory, Graz University of Technology, Kopernikusgasse 24/II, 8010, Graz, Austria

    Wöden Kusner

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  1. Yoav Kallus
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  2. Wöden Kusner
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Correspondence to Yoav Kallus.

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Editor in Charge: Günter M. Ziegler

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Kallus, Y., Kusner, W. The Local Optimality of the Double Lattice Packing. Discrete Comput Geom 56, 449–471 (2016). https://doi.org/10.1007/s00454-016-9792-4

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  • DOI: https://doi.org/10.1007/s00454-016-9792-4

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