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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Acknowledgements
The authors would like to thank the referees for their careful reading and valuable comments which have helped us to improve our manuscript. The first author was supported by JSPS KAKENHI Grant Numbers JP16K05120, JP20K03576. The second author was supported by JSPS KAKENHI Grant Number JP18K03356.
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Iriyeh, H., Shibata, M. Minimal Volume Product of Three Dimensional Convex Bodies with Various Discrete Symmetries. Discrete Comput Geom 68, 738–773 (2022). https://doi.org/10.1007/s00454-021-00357-6
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DOI: https://doi.org/10.1007/s00454-021-00357-6