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arXiv · 2007.08736

Minimal volume product of three dimensional convex bodies with various discrete symmetries

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 a discrete subgroup of $O(3)$ in several cases. We also characterize the convex bodies with the minimal volume product in each case. In particular, this provides a new partial result of the non-symmetric version of Mahler's conjecture in the three dimensional case.

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Hiroshi Iriyeh, Masataka Shibata. 2020-07-17. Minimal volume product of three dimensional convex bodies with various discrete symmetries. https://arxiv.org/abs/2007.08736

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