论文标题
具有某些离散对称性及其应用的凸体的最小量产物
Minimal volume product of convex bodies with certain discrete symmetries and its applications
论文作者
论文摘要
我们给出了$ n $二维凸体的音量产物的急剧下限，这些凸体是在离散子组$ so（k）= \ {g \ in So（n）中不变的； g（k）= k \} $，其中$ k $是$ n $ cube或$ n $ -simplex。这为Mahler的猜想及其非对称版本提供了新的部分结果。此外，我们从Mahler的猜想的角度给出了Viterbo的同型构想中的Insoperimetty类型的部分答案。
We give the sharp lower bound of the volume product of $n$-dimensional convex bodies which are invariant under a discrete subgroup $SO(K)=\{ g \in SO(n); g(K)=K \}$, where $K$ is an $n$-cube or $n$-simplex. This provides new partial results of Mahler's conjecture and its non-symmetric version. In addition, we give partial answers for Viterbo's isoperimetric type conjecture in symplectic geometry from the view point of Mahler's conjecture.
