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

  • Radosław Adamczak

    Uniwersytet Warszawski, Warszawa, Poland

  • Grigoris Paouris

    Texas A&M University, Texas, USA; Princeton University, Princeton, USA

  • Peter Pivovarov

    University of Missouri, Columbia, USA

  • Paul Simanjuntak

    University of Missouri, Columbia, USA; Texas A&M University, Texas, USA
From intersection bodies to dual centroid bodies: A stochastic approach to isoperimetry cover

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Abstract

We establish a family of isoperimetric inequalities for sets that interpolate between intersection bodies and dual -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.

Cite this article

Radosław Adamczak, Grigoris Paouris, Peter Pivovarov, Paul Simanjuntak, From intersection bodies to dual centroid bodies: A stochastic approach to isoperimetry. J. Eur. Math. Soc. (2024), published online first

DOI 10.4171/JEMS/1570