Beiträge zur Algebra und Geometrie
Contributions to Algebra and Geometry
Vol. 39, No. 2, pp. 473-479 (1998)

The Minimum Mean Width Translation Cover for Sets of Diameter One

Karoly Bezdek, Robert Connelly

Eötvös University, Institute of Mathematics II, Department of Geometry, H-1088 Budapest, Rakoczi ut 5, Hungary e-mail:,

Cornell University, Department of Mathematics, White Hall, Ithaca, NY 14853-7901, USA, e-mail:

Abstract: In this note we prove that the minimum mean width translation cover for all sets of diameter one in $E^d$ is the $d$-dimensional ball of diameter $\sqrt{2d\over d+1}$. This generalizes a well-known theorem of Jung [BF].

{\parindent25pt \item{[BF]} Bonnesen, T.; Fenchel, W.: Theorie der konvexen Körper. Springer, Berlin 1934; English translation: BCS Associates, Moscow, Idaho, 1987.


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