PAPER / ARXIV:2609.12714
Gergely Ambrus , Barnabás Gárgyán
RESUMO
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.
NO MESMO MAPA