On coverings of spheres by convex sets
type: Item
instance of: scholarly article
title: On coverings of spheres by convex sets
zbMATH Open document ID: 0551.52007
DOI: 10.1007/BF01193827
published in: Archiv der Mathematik
publication date: 1983-01-01T00:00:00Z
review text: Continuing his earlier investigations on coverings of the Euclidean space by congruent copies of given convex sets [Am. Math. Mon. 87, 286-287 (1980; see the preceding review), Mathematika 29, 18-31 (1982; Zbl 0496.52011), J. Comb. Theory, Ser. A 34, 71-79 (1983; Zbl 0509.52006)] the author proves the following result: Given a sequence of closed convex subsets of the n-dimensional unit sphere \(S^ n\) such that the sum of their n-dimensional measures exceeds a certain constant depending only on n, the convex sets can be rotated such as to cover \(S^ n\). For \(n=2\) and in case the geodesic diameters of the convex sets have small upper bounds, there are more precise results. These results are all closely connected with the problem of covering Euclidean space by congruent copies of given unbounded convex sets.
reviewed by: Peter M. Gruber
Mathematics Subject Classification ID: 52C17
Mathematics Subject Classification ID: 52A20
Mathematics Subject Classification ID: 52A40
Mathematics Subject Classification ID: 52A99
zbMATH DE Number: 3877888
zbMATH Keywords: spherical convex sets
zbMATH Keywords: coverings of the sphere
author: Helmut Groemer
MaRDI profile type: Publication
cites work: Q5820676
cites work: On Finite Classes of Convex Sets that Permit Space Coverings
cites work: Covering and packing properties of bounded sequences of convex sets
cites work: On space coverings by unbounded convex sets
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description: scientific article; zbMATH DE number 3877888