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arXiv · 2211.16263

From intersection bodies to dual centroid bodies: a stochastic approach to isoperimetry

Radoslaw Adamczak·Grigoris Paouris·Peter Pivovarov·Paul Simanjuntak
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Abstract

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 intersection inequality and the Lutwak--Zhang inequality. The approach depends on new empirical versions of these inequalities.

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Radoslaw Adamczak, Grigoris Paouris, Peter Pivovarov, Paul Simanjuntak. 2022-11-29. From intersection bodies to dual centroid bodies: a stochastic approach to isoperimetry. https://arxiv.org/abs/2211.16263

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