1 citations · 2 across the 7 of their papers we have counts for
8 papers
Negative moments of the support function and applications to isotropic convex bodies
Antonios Hmadi, Dimitris-Marios Liakopoulos
We study lower tails of support functions of isotropic convex bodies. An endpoint negative moment estimate, combined with a spherical cap argument, gives polynomial deviation estim…
Moment comparisons, Sudakov inequalities and entropy of centroid bodies
Antonios Hmadi, Dimitris-Marios Liakopoulos
Let be an isotropic log-concave random vector in and let be standard Gaussian. Starting from the first moment comparison for gauges, we derive corresponding…
Sharp Estimates for some Integral-Geometric Quantities Related To Transversality, Curvature And Visibility
Silouanos Brazitikos, Dimitris-Marios Liakopoulos
We investigate integral-geometric quantities arising from harmonic analysis which measure visibility and transversality. Motivated by their applications in multilinear Kakeya probl…
Inequalities for the quermassintegrals of sections of convex bodies
Dimitris-Marios Liakopoulos
We provide general estimates which compare the quermassintegrals of a convex body in with the averages of the corresponding quermassintegrals of the -codimen…
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 $…
Reverse Brascamp-Lieb inequality and the dual Bollobas-Thomason inequality
Dimitris-Marios Liakopoulos
The purpose of this article is to establish the dual version of the uniform cover inequality of Bollobas and Thomason.
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…
Estimates for measures of lower dimensional sections of convex bodies
Giorgos Chasapis, Apostolos Giannopoulos, Dimitris-Marios Liakopoulos
We present an alternative approach to some results of Koldobsky on measures of sections of symmetric convex bodies, which allows us to extend them to the not necessarily symmetric…