37 citations · 144 across the 42 of their papers we have counts for
5 papers · 1 filter
Estimating volume and surface area of a convex body via its projections or sections
Alexander Koldobsky, Christos Saroglou, Artem Zvavitch
The main goal of this paper is to present a series of inequalities connecting the surface area measure of a convex body and surface area measure of its projections and sections. We…
Volume difference inequalities
Apostolos Giannopoulos, Alexander Koldobsky
We prove several inequalities estimating the distance between volumes of two bodies in terms of the maximal or minimal difference between areas of sections or projections of these…
Inequalities for the surface area of projections of convex bodies
Apostolos Giannopoulos, Alexander Koldobsky, Petros Valettas
We provide general inequalities that compare the surface area S(K) of a convex body K in to the minimal, average or maximal surface area of its hyperplane or lower…
Variants of the Busemann-Petty problem and of the Shephard problem
Apostolos Giannopoulos, Alexander Koldobsky
We provide an affirmative answer to a variant of the Busemann-Petty problem, proposed by V.~Milman: Let be a convex body in and let be a compact subset of $…
A remark on measures of sections of -balls
Alexander Koldobsky, Alain Pajor
We show that the slicing problem holds true for subspaces of in the setting of arbitrary measures in place of volume. This generalizes a result of Milman for the original…