Beiträge zur Algebra und Geometrie
Contributions to Algebra and Geometry
Vol. 51, No. 1, pp. 229-235 (2010)
Covering large balls with convex sets in spherical space
Károly Bezdek and Rolf SchneiderDepartment of Mathematics and Statistics, University of Calgary, 2500 University Drive N.W., AB, Canada, T2N 1N4, e-mail: firstname.lastname@example.org; Mathematisches Institut, Albert-Ludwigs-Universität, Eckerstr. 1, D-79104 Freiburg i. Br., Germany, e-mail: email@example.com
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.