Beitr\ EMIS ELibM Electronic Journals Beiträge zur Algebra und Geometrie
Contributions to Algebra and Geometry
Vol. 51, No. 1, pp. 229-235 (2010)

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Covering large balls with convex sets in spherical space

Károly Bezdek and Rolf Schneider

Department of Mathematics and Statistics, University of Calgary, 2500 University Drive N.W., AB, Canada, T2N 1N4, e-mail: bezdek@math.ucalgary.ca; Mathematisches Institut, Albert-Ludwigs-Universität, Eckerstr. 1, D-79104 Freiburg i. Br., Germany, e-mail: rolf.schneider@math.uni-freiburg.de

Abstract: If the $n$-dimensional unit sphere is covered by finitely many spherically convex bodies, then the sum of the inradii of these bodies is at least $\pi$. This bound is sharp, and the equality case is characterized.

Keywords: spherical coverings, plank problem, spherical volume, inradius

Classification (MSC2000): 52A55, 52C17

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Electronic version published on: 27 Jan 2010. This page was last modified: 28 Jan 2013.

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