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arXiv · 2409.14214

On the volume of sums of anti-blocking bodies

Auttawich Manui·Cheikh Saliou Ndiaye·Artem Zvavitch
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Abstract

We study inequalities on the volume of Minkowski sum in the class of anti-blocking bodies. We prove analogues of Pl\"unnecke-Ruzsa type inequality and V. Milman inequality on the concavity of the ratio of volumes of bodies and their projections. We also study Firey $L_p-$sums of anti-blocking bodies and prove Pl\"unnecke-Ruzsa type inequality; V. Milman inequality and Roger-Shephard inequality. The sharp constants are provided in all of those inequalities, for the class of anti-blocking bodies. Finally, we extend our results to the case of unconditional product measures with decreasing density.

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Auttawich Manui, Cheikh Saliou Ndiaye, Artem Zvavitch. 2024-09-21. On the volume of sums of anti-blocking bodies. https://doi.org/10.1142/s0219199725500956

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