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arXiv · 1106.5635

Kadets type theorems for partitions of a convex body

Arseniy Akopyan·Roman Karasev
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Abstract

For convex partitions of a convex body $B$ we prove that we can put a homothetic copy of $B$ into each set of the partition so that the sum of homothety coefficients is $\ge 1$. In the plane the partition may be arbitrary, while in higher dimensions we need certain restrictions on the partition.

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Arseniy Akopyan, Roman Karasev. 2011-11-21. Kadets type theorems for partitions of a convex body. https://doi.org/10.1007/s00454-012-9437-1

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