Geodesic
Geodesic diameter of bodies of constant width
Zapiski Nauchnykh Seminarov POMI, Geometry and topology. Part 10, Tome 353 (2008), pp. 35-38

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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. 
@article{ZNSL_2008_353_a3,
     author = {V. A. Zalgaller},
     title = {Geodesic diameter of bodies of constant width},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {35--38},
     publisher = {mathdoc},
     volume = {353},
     year = {2008},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2008_353_a3/}
}
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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/