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An Isoperimetric Inequality for Planar Triangulations

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Abstract

We prove a discrete analogue to a classical isoperimetric theorem of Weil for surfaces with non-positive curvature. It is shown that hexagons in the triangular lattice have maximal volume among all sets of a given boundary in any triangulation with minimal degree 6.

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Acknowledgements

OA is supported in part by NSERC. We thank Nicolas Curien for a suggested simplification and a referee for careful review and comments.

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Authors and Affiliations

  1. University of British Columbia, Vancouver, BC, V6T 1Z2, Canada

    Omer Angel

  2. Department of Mathematics, The Weizmann Institute of Science, 7610001, Rehovot, Israel

    Itai Benjamini

  3. Intel Corp., Haifa, Israel

    Nizan Horesh

Authors
  1. Omer Angel
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  2. Itai Benjamini
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  3. Nizan Horesh
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Correspondence to Omer Angel.

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Editors in Charge: Günter M. Ziegler, János Pach

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Angel, O., Benjamini, I. & Horesh, N. An Isoperimetric Inequality for Planar Triangulations. Discrete Comput Geom 59, 802–809 (2018). https://doi.org/10.1007/s00454-017-9942-3

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  • DOI: https://doi.org/10.1007/s00454-017-9942-3

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