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Minimal central slices of the regular simplex
Abstract
We prove that minimal-volume hyperplane sections of the regular simplex through its centroid are parallel to a facet. The proof combines variational methods with Fourier-analytic techniques and zero-diminishing arguments to show that every critical normal vector has at most three distinct non-zero coordinates. Analysis of the two- and three-value cases then yields the sharp lower bound.
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BibTeX
@misc{ambrus2026minimal,
title = {{Minimal central slices of the regular simplex}},
author = {Gergely Ambrus and Barnabás Gárgyán},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.12714},
eprint = {2609.12714},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.12714},
}
RIS
TY - UNPB
TI - Minimal central slices of the regular simplex
AU - Gergely Ambrus
AU - Barnabás Gárgyán
PY - 2026
DA - 2026/09/22
PB - arXiv
DO - 10.48550/arxiv.2609.12714
UR - https://arxiv.org/abs/2609.12714
AB - We prove that minimal-volume hyperplane sections of the regular simplex through its centroid are parallel to a facet. The proof combines variational methods with Fourier-analytic techniques and zero-diminishing arguments to show that every critical normal vector has at most three distinct non-zero coordinates. Analysis of the two- and three-value cases then yields the sharp lower bound.
ER -