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On a theorem of G. D. Chakerian

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Abstract:

Among all bodies of constant width in the Euclidean plane, a Reuleaux triangle of width $lambda$ has minimal area. But Reuleaux triangles are also minimal in another sense: if a convex body can be covered by a translate of any Reuleaux triangle, then it can be covered by a translate of any convex body of the same constant width. The first result is known as the Blaschke-Lebesgue theorem, and it is extended to an arbitrary normed plane in [19] and [5]. In the present paper we extend the second minimal property, known as Chakerian’s theorem, to all normed planes. Some corollaries from this generalization are also given.

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