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arXiv · 1608.07084

Strengthened volume inequalities for L_p zonoids of even isotropic measures

Karoly J. Boroczky·Ferenc Fodor·Daniel Hug
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Abstract

We strengthen the volume inequalities for L_p zonoids of even isotropic measures and for their duals, which are due to Ball, Barthe and Lutwak, Yang, Zhang. Along the way, we prove a stronger version of the Brascamp-Lieb inequality for a family of functions that can approximate arbitrary well some Gaussians when equality holds. The special case p=\infty yields a stability version of the reverse isoperimetric inequality for centrally symmetric bodies.

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Karoly J. Boroczky, Ferenc Fodor, Daniel Hug. 2016-08-25. Strengthened volume inequalities for L_p zonoids of even isotropic measures. https://doi.org/10.1090/tran/7299

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