论文标题
具有各种离散对称性的三维凸体的最小体积产物
Minimal volume product of three dimensional convex bodies with various discrete symmetries
论文作者
论文摘要
我们给出了三维凸体的体积乘积的急剧下限，这些凸形物体在几种情况下在$ o（3）$的离散子组下是不变的。在每种情况下，我们还用最少的体积产物来表征凸形体。特别是，这为Mahler在三维情况下的猜想的非对称版本提供了新的部分结果。
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.
