Minimal volume product of three dimensional convex bodies with various discrete symmetries
Metric Geometry
2020-10-09 v2
Abstract
We give the sharp lower bound of the volume product of three dimensional convex bodies which are invariant under a discrete subgroup of 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.
Cite
@article{arxiv.2007.08736,
title = {Minimal volume product of three dimensional convex bodies with various discrete symmetries},
author = {Hiroshi Iriyeh and Masataka Shibata},
journal= {arXiv preprint arXiv:2007.08736},
year = {2020}
}
Comments
29 pages, some minor changes