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Journal of Convex Analysis 29 (2022), No. 3, 921--928
Copyright Heldermann Verlag 2022

Approximation of Spherical Bodies of Constant Width and Reduced Bodies

Marek Lassak
University of Science and Technology, Bydgoszcz, Poland

We present a spherical version of the theorem of Blaschke that every body of constant width w < π/2 can be approximated by a body of constant width w whose boundary consists only of pieces of circles of radius w as well as we wish in the sense of the Hausdorff distance. This is a special case of our theorem about approximation of spherical reduced bodies.

Keywords: Sphere, spherical convex body, body of constant width, reduced body, Hausdorff distance, approximation.

MSC: 52A55.

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