4 citations · 6 across the 11 of their papers we have counts for
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Empirical dual volumes
Grigoris Paouris, Peter Pivovarov, Paul Simanjuntak
We introduce an empirical version of dual volumes within dual Brunn--Minkowski theory. These provide a simple model for computation and analysis under symmetrization, including mom…
Empirical forms of the Petty projection inequality
Grigoris Paouris, Peter Pivovarov, Kateryna Tatarko
The Petty projection inequality is a fundamental affine isoperimetric principle for convex sets. It has shaped several directions of research in convex geometry which forged new co…
From intersection bodies to dual centroid bodies: a stochastic approach to isoperimetry
Radoslaw Adamczak, Grigoris Paouris, Peter Pivovarov +1
We establish a family of isoperimetric inequalities for sets that interpolate between intersection bodies and dual Lp centroid bodies. This provides a bridge between the Busemann i…
Stochastic forms of Brunn's principle
P. Pivovarov, J. Rebollo Bueno
A number of geometric inequalities for convex sets arising from Brunn's concavity principle have recently been shown to yield local stochastic formulations. Comparatively, there ha…
A stochastic Prekopa-Leindler inequality for log-concave functions
Peter Pivovarov, Jesus Rebollo Bueno
The Brunn-Minkowski and Prékopa-Leindler inequalities admit a variety of proofs that are inspired by convexity. Nevertheless, the former holds for compact sets and the latter for i…
Spherical centroid bodies
Florian Besau, Thomas Hack, Peter Pivovarov +1
The spherical centroid body of a centrally-symmetric convex body in the Euclidean unit sphere is introduced. Two alternative definitions - one geometric, the other probabilistic in…
Affine isoperimetric inequalities on flag manifolds
Susanna Dann, Grigoris Paouris, Peter Pivovarov
Building on work of Furstenberg and Tzkoni, we introduce -flag affine quermassintegrals and their dual versions. These quantities generalize affine and dual affine quermas…
On a quantitative reversal of Alexandrov's inequality
Grigoris Paouris, Peter Pivovarov, Petros Valettas
Alexandrov's inequalities imply that for any convex body , the sequence of intrinsic volumes is non-increasing (when suitably normalized). Milman's random…
Randomized isoperimetric inequalities
Grigoris Paouris, Peter Pivovarov
We discuss isoperimetric inequalities for convex sets. These include the classical isoperimetric inequality and that of Brunn-Minkowski, Blaschke-Santalo, Busemann-Petty and their…
Random ball-polyhedra and inequalities for intrinsic volumes
Grigoris Paouris, Peter Pivovarov
We prove a randomized version of the generalized Urysohn inequality relating mean-width to the other intrinsic volumes. To do this, we introduce a stochastic approximation procedur…
Volume of the polar of random sets and shadow systems
Dario Cordero-Erausquin, Matthieu Fradelizi, Grigoris Paouris +1
We obtain optimal inequalities for the volume of the polar of random sets, generated for instance by the convex hull of independent random vectors in Euclidean space. Extremizers a…