Projective transformations of convex bodies and volume product

Florent Balacheff; Gil Solanes; Kroum Tzanev

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arXiv · 2303.17794

Projective transformations of convex bodies and volume product

Florent Balacheff·Gil Solanes·Kroum Tzanev

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Abstract

In this paper we study certain variational aspects of the volume product functional restricted to the space of small projective deformations of a fixed convex body. In doing so, we provide a short proof of a theorem by Klartag: a strong version of the slicing conjecture implies the Mahler conjecture. We also exhibit an interesting family of critical convex bodies in dimension $2$ containing saddle points for this functional.

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Florent Balacheff, Gil Solanes, Kroum Tzanev. 2023-03-31. Projective transformations of convex bodies and volume product. https://arxiv.org/abs/2303.17794

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