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A solution of Hadwiger's covering problem for zonoids

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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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Authors and Affiliations

  1. Institute of System Analysis RAN, Pr. 60 Let Oktjabrja 9, 117312, Moscow, Russia

    V. G. Boltjanski

  2. Parlament of Resp. Moldova, Pr. Stefan kel Mare 154, 277000, Kishinev, Moldova

    P. S. Soltan

Authors
  1. V. G. Boltjanski
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  2. P. S. Soltan
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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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  • DOI: https://doi.org/10.1007/BF01305231

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