入江 博

Abstract We give the sharp lower bound of the volume product of $n$-dimensional convex bodies that are invariant under the discrete subgroups $SO(K)=\{ g \in SO(n); g(K)=K \}$, where $K$ is an $n$-cube or $n$-simplex. This provides new partial results of Mahler’s conjecture and its nonsymmetric version. In addition, we give partial answers for Viterbo’s isoperimetric-type conjecture in symplectic geometry from the view point of Mahler’s conjecture.