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.
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