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Volumetric bounds for intersections of congruent balls in Euclidean spaces

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Abstract

We investigate the intersections of balls of radius r, called r-ball bodies, in Euclidean d-space. An r-lense (resp., r-spindle) is the intersection of two balls of radius r (resp., balls of radius r containing a given pair of points). We prove that among r-ball bodies of a given volume, the r-lense (resp., r-spindle) has the smallest inradius (resp., largest circumradius). In general, we upper (resp., lower) bound the intrinsic volumes of r-ball bodies of a given inradius (resp., circumradius). This complements and extends some earlier results on volumetric estimates for r-ball bodies.

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Authors and Affiliations

  1. Department of Mathematics and Statistics, University of Calgary, Calgary, Canada

    Károly Bezdek

  2. Department of Mathematics, University of Pannonia, Veszprém, Hungary

    Károly Bezdek

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  1. Károly Bezdek
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Correspondence to Károly Bezdek.

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Partially supported by a Natural Sciences and Engineering Research Council of Canada Discovery Grant.

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Bezdek, K. Volumetric bounds for intersections of congruent balls in Euclidean spaces. Aequat. Math. 95, 653–665 (2021). https://doi.org/10.1007/s00010-021-00814-w

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  • DOI: https://doi.org/10.1007/s00010-021-00814-w

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