Brunn-Minkowski and Reverse Isoperimetric Inequalities for Dual Quermassintegrals

Shay Sadovsky; Gaoyong Zhang

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arXiv · 2505.23748

Brunn-Minkowski and Reverse Isoperimetric Inequalities for Dual Quermassintegrals

Shay Sadovsky·Gaoyong Zhang

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Abstract

This paper establishes two new geometric inequalities in the dual Brunn-Minkowski theory. The first, originally conjectured by Lutwak, is the Brunn-Minkowski inequality for dual quermassintegrals of origin-symmetric convex bodies. The second, generalizing Ball's volume ratio inequality, is a reverse isoperimetric inequality: among all origin-symmetric convex bodies in John's position, the cube maximizes the dual quermassintegrals.

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Shay Sadovsky, Gaoyong Zhang. 2025-05-29. Brunn-Minkowski and Reverse Isoperimetric Inequalities for Dual Quermassintegrals. https://arxiv.org/abs/2505.23748

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