English

A generalization of Bang's lemma

Metric Geometry 2022-06-06 v4 Functional Analysis

Abstract

We prove a common extension of Bang's and Kadets' lemmas for contact pairs, in the spirit of the Colourful Carath\'eodory Theorem. We also formulate a generalized version of the affine plank problem and prove it under special assumptions. In particular, we obtain a generalization of Kadets' theorem. Finally, we give applications to problems regarding translative and homothetic coverings.

Keywords

Cite

@article{arxiv.2201.08823,
  title  = {A generalization of Bang's lemma},
  author = {Gergely Ambrus},
  journal= {arXiv preprint arXiv:2201.08823},
  year   = {2022}
}

Comments

7 pages, 1 figure. An extension of V. Soltan's conjecture by G. Fejes Toth is added, minor typos corrected

R2 v1 2026-06-24T08:58:02.929Z