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arXiv · 2608.06081

Empirical dual volumes

Grigoris Paouris·Peter Pivovarov·Paul Simanjuntak
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Abstract

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 moment inequalities. As an application, we derive a new proof of the Busemann intersection inequality that relies on counting points in slabs rather than working directly with volumes of slices.

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Grigoris Paouris, Peter Pivovarov, Paul Simanjuntak. 2026-08-06. Empirical dual volumes. https://arxiv.org/abs/2608.06081

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