141 citations · 238 across the 33 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…
Optimal mean width and metric entropy estimates for convex bodies
Grigoris Paouris, Reese Pathak
We show that for any and any convex body , there exists such that \[ \mathrm{diam}(TK) \lesssim \sqrt{n} \mathrm{vr}(K), \…
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…
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…