3 papers
math.FA2020
Non-central sections of the simplex, the cross-polytope and the cube
Hermann König
We determine the maximal hyperplane sections of the regular -simplex, if the distance of the hyperplane to the centroid is fairly large, i.e. larger than the distance of the cen…
math.MG2019
On the volume of non-central sections of a cube
Hermann König, Mark Rudelson
Let be the cube of side length one centered at the origin in , and let be an affine -dimensional subspace of having distance to the or…
math.MG2018
On the maximal perimeter of sections of the cube
Hermann Koenig, Alexander Koldobsky
We prove that the (n-2)-dimensional surface area (perimeter) of central hyperplane sections of the n-dimensional unit cube is maximal for the hyperplane perpendicular to the vector…