Projective transformations of convex bodies and volume product
Metric Geometry
2023-04-03 v1 Differential Geometry
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 containing saddle points for this functional.
Keywords
Cite
@article{arxiv.2303.17794,
title = {Projective transformations of convex bodies and volume product},
author = {Florent Balacheff and Gil Solanes and Kroum Tzanev},
journal= {arXiv preprint arXiv:2303.17794},
year = {2023}
}
Comments
10 pages, 3 figures