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arXiv · 1511.03381

Iterations of the projection body operator and a remark on Petty's conjectured projection inequality

Christos Saroglou·Artem Zvavitch
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Abstract

We prove that if a convex body has absolutely continuous surface area measure, whose density is sufficiently close to the constant, then the sequence $\{\Pi^mK\}$ of convex bodies converges to the ball with respect to the Banach-Mazur distance, as $m\rightarrow\infty$. Here, $\Pi$ denotes the projection body operator. Our result allows us to show that the ellipsoid is a local solution to the conjectured inequality of Petty and to improve a related inequality of Lutwak.

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Christos Saroglou, Artem Zvavitch. 2015-11-11. Iterations of the projection body operator and a remark on Petty's conjectured projection inequality. https://arxiv.org/abs/1511.03381

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