Kadets type theorems for partitions of a convex body

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.

References in corpus (1)

• The plank problem for symmetric bodies

Cited by in corpus (2)

• Proof of László Fejes Tóth's zone conjecture
• A cap covering theorem