3 papers
math.MG2026
Minimal central slices of the regular simplex
Gergely Ambrus, Barnabás Gárgyán
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 t…
math.MG2024
Estimates on the decay of the Laplace-Polya integral
Gergely Ambrus, Barnabás Gárgyán
The Laplace--Pólya integral, defined by , appears in several areas of mathematics. We study this q…
math.MG2023
Non-diagonal critical central sections of the cube
Gergely Ambrus, Barnabás Gárgyán
We study the -dimensional volume of central hyperplane sections of the -dimensional cube . Our main goal is two-fold: first, we provide an alternative, simpler argum…