English

The plank problem for symmetric bodies

Metric Geometry 2009-10-22 v1 Functional Analysis

Abstract

Given a symmetric convex body CC and nn hyperplanes in an Euclidean space, there is a translate of a multiple of CC, at least 1n+1{1\over n+1} times as large, inside CC, whose interior does not meet any of the hyperplanes. The result generalizes Bang's solution of the plank problem of Tarski and has applications to Diophantine approximation.

Keywords

Cite

@article{arxiv.math/9201218,
  title  = {The plank problem for symmetric bodies},
  author = {Keith Ball},
  journal= {arXiv preprint arXiv:math/9201218},
  year   = {2009}
}