Extensions of polynomial plank covering theorems

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 versio...

Full description

Saved in:
Bibliographic Details
Published in:The Bulletin of the London Mathematical Society 2024-03, Vol.56 (3), p.1014-1028
Main Authors: Glazyrin, Alexey, Karasev, Roman, Polyanskii, Alexander
Format: Article
Language:English
Citations: Items that this one cites
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary: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.
ISSN:0024-6093
1469-2120
DOI:10.1112/blms.12979