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A Characterization of the Disc by the Angle of the Support Cone

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Abstract

Let K be a body in the plane and let \(\lambda <1\) be a positive real number. Suppose that for every \(x\in \mathbb R^2\) such that \(\lambda K + x\) is exteriorly tangent to K, the common support cone of K and \(\lambda K + x\) has a constant angle \(\alpha \). Suppose that one of the following conditions is satisfied: (a) K is a body of constant width, (b) K is centrally symmetric. Then K is a Euclidean disc.

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  1. Facultad de Ingeniería, Universidad Autónoma de Querétaro, Cerro de las Campanas s/n, C.P. 76010, Querétaro, Mexico

    Jesús Jerónimo-Castro

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  1. Jesús Jerónimo-Castro
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Correspondence to Jesús Jerónimo-Castro.

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Jerónimo-Castro, J. A Characterization of the Disc by the Angle of the Support Cone. Results Math 76, 130 (2021). https://doi.org/10.1007/s00025-021-01446-x

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