English

Kadets type theorems for partitions of a convex body

Combinatorics 2012-12-27 v2 Functional Analysis

Abstract

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

Keywords

Cite

@article{arxiv.1106.5635,
  title  = {Kadets type theorems for partitions of a convex body},
  author = {Arseniy Akopyan and Roman Karasev},
  journal= {arXiv preprint arXiv:1106.5635},
  year   = {2012}
}