PreprintarXiv licencearXiv
A short proof of Ball's plank theorem
Abstract
We give a short proof of the following theorem of K. Ball: If a centrally symmetric convex body K⊂ ℝd is covered by finitely many planks, then the sum of their relative widths with respect to K is at least $1$.
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BibTeX
@misc{akopyan2026short,
title = {{A short proof of Ball's plank theorem}},
author = {Arseniy Akopyan and Alexander Polyanskii},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.36163},
eprint = {2609.36163},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.36163},
}
RIS
TY - UNPB
TI - A short proof of Ball's plank theorem
AU - Arseniy Akopyan
AU - Alexander Polyanskii
PY - 2026
DA - 2026/09/28
PB - arXiv
DO - 10.48550/arxiv.2609.36163
UR - https://arxiv.org/abs/2609.36163
AB - We give a short proof of the following theorem of K. Ball: If a centrally symmetric convex body K⊂ ℝ^d is covered by finitely many planks, then the sum of their relative widths with respect to K is at least $1$.
ER -