This is an announcement for the paper "Kadets type theorems for partitions of a convex body" by Arseniy Akopyan and Roman Karasev.

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.

Archive classification: math.CO math.FA

Mathematics Subject Classification: 52C15, 52C17, 52A40, 52A21

Submitted from: r_n_karasev@mail.ru

The paper may be downloaded from the archive by web browser from URL

http://front.math.ucdavis.edu/1106.5635

or

http://arXiv.org/abs/1106.5635