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Journal of Convex Analysis 19 (2012), No. 3, 865--874
Copyright Heldermann Verlag 2012

Approximation of Bodies of Constant Width and Reduced Bodies in a Normed Plane

Marek Lassak
Institute of Mathematics and Physics, University of Technology and Life Sciences, al. Kaliskiego 7, Bydgoszcz 85--789, Poland

We prove that for every ε > 0 and for every convex body of constant width in a normed plane there exists a convex body of the same constant width whose boundary consists only of arcs of circles in the sense of the norm such that the Hausdorff distance between the two bodies is at most ε. This generalizes the Euclidean case proved by Blaschke. We also present a more general theorem about approximation of reduced bodies.

Keywords: Reduced convex body, body of constant width, normed plane, Hausdorff distance, approximation.

MSC: 52A10, 52A21, 52A27, 46B25

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