Geodesic
Geodesic diameter of bodies of constant width
Zapiski Nauchnykh Seminarov POMI, Geometry and topology. Part 10, Tome 353 (2008), pp. 35-38 
V. A. Zalgaller. Geodesic diameter of bodies of constant width. Zapiski Nauchnykh Seminarov POMI, Geometry and topology. Part 10, Tome 353 (2008), pp. 35-38. http://geodesic.mathdoc.fr/item/ZNSL_2008_353_a3/
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     title = {Geodesic diameter of bodies of constant width},
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     url = {http://geodesic.mathdoc.fr/item/ZNSL_2008_353_a3/}
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Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

The geodesic diameter $G$ of the surface of a three-dimensional body $\Phi$ of constant width $B$ is estimated via $B$ from above and from below. It is proved that $G\le\frac\pi2B$, where an equality occurs if and only if $\Phi$ is a body of revolution. Bibl. – 3 titles.

[1] T. Bonnezen, V. Fenkhel, Teoriya vypuklykh tel, Fazis, M., 2002

[2] Yu. V. Burago, V. A. Zalgaller, “Izoperimetricheskaya zadacha pri ogranichenii shiriny oblasti na poverkhnosti”, Tr. Matem. inst. im. V. A. Steklova, 76, Nauka, M., 1965, 81–87 | MR

[3] E. Meissner, “Über Punktmengen konstanter Breite”, Wissenschr. Naturforsch. Ges. Zürich, 56 (1911), 42–50 | Zbl