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arXiv · 2409.16785

Minimal volume product of three dimensional convex bodies invariant under certain groups of order four

Hiroshi Iriyeh·Masataka Shibata
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Abstract

We give the sharp lower bound of the volume product of three dimensional convex bodies which are invariant under two kinds of discrete subgroups of $O(3)$ of order four. We also characterize the convex bodies with the minimal volume product in each case. This provides new partial results of the non-symmetric version of Mahler's conjecture in the three dimensional case.

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Hiroshi Iriyeh, Masataka Shibata. 2024-09-25. Minimal volume product of three dimensional convex bodies invariant under certain groups of order four. https://arxiv.org/abs/2409.16785

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