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math.MG2026
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…
math.MG2026
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), \…