PreprintCC BY 4.0arXiv
A remark on projection outer volume ratio
Abstract
We study the projection outer volume ratio povrk(K) introduced by D. Galicer, A.E. Litvak, M. Merzbacher, and D. Pinasco. When k≤ n/2, we provide sharp bounds in the general case, namely povrk(K)≤ C max{1, √(k/ln(2n/k))}, where the maximal order is obtained for K=B1n. Moreover, in the important particular case K=B2n we show that povrk(B2n) is bounded by an absolute constant whenever k≤ n/2 and povrk(B2n)≤ C√(n/(n−k)) ln(1+n/(n−k)) for k>n/2. The latter bound is sharp up to a logarithmic term.
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BibTeX
@misc{litvak2026remark,
title = {{A remark on projection outer volume ratio}},
author = {A. E. Litvak},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.09562},
eprint = {2610.09562},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.09562},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - A remark on projection outer volume ratio
AU - A. E. Litvak
PY - 2026
DA - 2026/10/07
PB - arXiv
DO - 10.48550/arxiv.2610.09562
UR - https://arxiv.org/abs/2610.09562
AB - We study the projection outer volume ratio povr_k(K) introduced by D. Galicer, A.E. Litvak, M. Merzbacher, and D. Pinasco. When k≤ n/2, we provide sharp bounds in the general case, namely povr_k(K)≤ C max{1, √(k/ln(2n/k))}, where the maximal order is obtained for K=B_1^n. Moreover, in the important particular case K=B_2^n we show that povr_k(B_2^n) is bounded by an absolute constant whenever k≤ n/2 and povr_k(B_2^n)≤ C√(n/(n−k)) ln(1+n/(n−k)) for k>n/2. The latter bound is sharp up to a logarithmic term.
ER -