Beitr\ EMIS ELibM Electronic Journals Beiträge zur Algebra und Geometrie
Contributions to Algebra and Geometry
Vol. 48, No. 1, pp. 217-224 (2007)

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Circumscribed simplices of minimal mean width

Károly Böröczky jr and Rolf Schneider

Alfréd Rényi Institute of Mathematics, Hungarian Academy of Sciences, H-1053 Budapest, Reáltanoda u. 13--15, Hungary, e-mail: carlos@renyi.hu; Mathematisches Institut, Albert-Ludwigs-Universität, Eckerstr. 1, D-79104 Freiburg i. Br., Germany, e-mail: rolf.schneider@math.uni-freiburg.de

Abstract: It is proved that the minimal mean width of all simplices circumscribed about a convex body of given mean width attains its maximum precisely if the body is a ball. An analogous result holds for circumscribed parallelepipeds, with balls replaced by bodies of constant width.

Classification (MSC2000): 52A20, 52A40

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Electronic version published on: 14 May 2007. This page was last modified: 27 Jan 2010.

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