5 papers · 1 filter
On a version of the slicing problem for the surface area of convex bodies
Silouanos Brazitikos, Dimitris-Marios Liakopoulos
We study the slicing inequality for the surface area instead of volume. This is the question whether there exists a constant depending (or not) on the dimension so that $…
Vector-Valued Maclaurin Inequalities
Silouanos Brazitikos, Finlay McIntyre
We investigate a Maclaurin inequality for vectors and its connection to an Aleksandrov-type inequality for parallelepipeds.
Sections of convex bodies in John's and minimal surface area position
David Alonso-Gutiérrez, Silouanos Brazitikos
We prove several estimates for the volume, mean width, and the value of the Wills functional of sections of convex bodies in John's position, as well as for their polar bodies. The…
Reverse Loomis-Whitney inequalities via isotropicity
David Alonso-Gutiérrez, Silouanos Brazitikos
Given a centered convex body , we study the optimal value of the constant such that there exists an orthonormal basis for whi…
Uniform cover inequalities for the volume of coordinate sections and projections of convex bodies
S. Brazitikos, A. Giannopoulos, D-M. Liakopoulos
The classical Loomis-Whitney inequality and the uniform cover inequality of Bollobás and Thomason provide lower bounds for the volume of a compact set in terms of its lower dimensi…