A solution of Hadwiger's covering problem for zonoids

Abstract

For a convex body M ⊂ ℝn byb(M) the least integerp is denoted, such that there are bodiesM 1, ...,M p each of which is homothetic toM with a positive ratiok<1 andM 1∪...∪M p M. H. Martini has proved [7] thatb(M)<-3·2n−2 for every zonotope M ⊂ ℝn, which is not a parallelotope.

In the paper this Martini's result is extended to zonoids. In the proof some notions and facts of real functions theory are used (points of density, approximative continuity).

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Boltjanski, V.G., Soltan, P.S. A solution of Hadwiger's covering problem for zonoids. Combinatorica 12, 381–388 (1992). https://doi.org/10.1007/BF01305231

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AMS Subject Classification code (1991)

  • 52 A 20