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The Filling Problem in the Cube

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Abstract

We prove an isoperimetric inequality for filling cellular \(\mathbb {Z}_2\)-cycles in a high-dimensional cube with cellular chains. In addition, we provide a family of cubical cellular cycles for which the exponent in the inequality is optimal.

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Acknowledgments

The author would like to thank Larry Guth for his suggestions and encouragement and Matt Kahle for providing the impetus to complete the project. Significant gratitude is due to the editor, who was remarkably patient when the author made a mess of the first round of revisions. The author would also like to thank the Institute for Advanced Study where the early stages of this work were completed.

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Authors and Affiliations

  1. Department of Mathematics, University of Chicago, Chicago, IL, USA

    Dominic Dotterrer

  2. University of Toronto, Toronto, ON, Canada

    Dominic Dotterrer

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  1. Dominic Dotterrer
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Correspondence to Dominic Dotterrer.

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Editor in Charge: Günter M. Ziegler

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Dotterrer, D. The Filling Problem in the Cube. Discrete Comput Geom 55, 249–262 (2016). https://doi.org/10.1007/s00454-015-9725-7

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  • DOI: https://doi.org/10.1007/s00454-015-9725-7

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