Abstract
A well-known problem of discrete geometry is due to Hadwiger (1957), (1960) and Levi (1955). The following conjecture concerning this problem was published by Hadwiger (1957), (1960) and also by Gohberg and Markus (1960): Any convex body of E d, d ≥ 1 (i.e. any compact convex subset of the d-dimensional Euclidean space E d with non-empty interior) can be covered by 2d smaller homothetic bodies and equality is attained only for d-dimensional parallelotopes. This conjecture has stimulated a lot of research in geometry. To survey the basic results we need some simple definitions.
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Bezdek, K. (1993). Hadwiger-Levi’s Covering Problem Revisited. In: Pach, J. (eds) New Trends in Discrete and Computational Geometry. Algorithms and Combinatorics, vol 10. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-58043-7_9
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DOI: https://doi.org/10.1007/978-3-642-58043-7_9
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