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Constant diameter and constant width of spherical convex bodies

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Abstract

In this paper we show that a spherical convex body C is of constant diameter \(\tau \) if and only if C is of constant width \(\tau \), for \(0<\tau <\pi \). Moreover, some applications to Wulff shapes are given.

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Acknowledgements

The authors thank the anonymous referees for their valuable comments of the original version of this paper. This work was supported, in partial, by Natural Science Basic Research Program of Shaanxi (Program Nos. 2020JQ-235, 2020JQ-236, 2019JQ-246), and the Initial Foundation for Scientific Research of Northwest A&F University (Program Nos. 2452018016, 2452018018).

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  1. College of Science, Northwest A&F University, Yangling, Shaanxi, China

    Huhe Han & Denghui Wu

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  1. Huhe Han
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  2. Denghui Wu
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Correspondence to Denghui Wu.

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Dedicated to Professor Takashi Nishimura on the occasion of his 60th birthday.

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Han, H., Wu, D. Constant diameter and constant width of spherical convex bodies. Aequat. Math. 95, 167–174 (2021). https://doi.org/10.1007/s00010-020-00740-3

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  • DOI: https://doi.org/10.1007/s00010-020-00740-3

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