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Unique determination of convex polytopes by non-central sections

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Abstract

A question of Barker and Larman asks whether convex bodies that contain a sphere of radius t in their interiors are uniquely determined by the volumes of sections by hyperplanes tangent to the sphere. We affirmatively solve this problem for convex polytopes.

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Authors and Affiliations

  1. Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, AB, T6G 2G1, Canada

    Vladyslav Yaskin

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  1. Vladyslav Yaskin
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Correspondence to Vladyslav Yaskin.

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V. Yaskin was partially supported by a grant from NSERC.

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Yaskin, V. Unique determination of convex polytopes by non-central sections. Math. Ann. 349, 647–655 (2011). https://doi.org/10.1007/s00208-010-0538-y

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  • DOI: https://doi.org/10.1007/s00208-010-0538-y

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