Extensions of polynomial plank covering theorems
Metric Geometry
2024-05-28 v2 Complex Variables
Functional Analysis
Abstract
We prove a complex polynomial plank covering theorem for not necessarily homogeneous polynomials. As the consequence of this result, we extend the complex plank theorem of Ball to the case of planks that are not necessarily centrally symmetric and not necessarily round. We also prove a weaker version of the spherical polynomial plank covering conjecture for planks of different widths.
Keywords
Cite
@article{arxiv.2211.10886,
title = {Extensions of polynomial plank covering theorems},
author = {Alexey Glazyrin and Roman Karasev and Alexandr Polyanskii},
journal= {arXiv preprint arXiv:2211.10886},
year = {2024}
}
Comments
Lemma 4.1 is corrected after the official publication, fortunately, not affecting the other results