A remark on the Mahler conjecture: local minimality of the unit cube

Fedor Nazarov, Fedor Petrov, Dmitry Ryabogin +1

We prove that the unit cube $B_{\infty }^n$ is a strict local minimizer for the Mahler volume product $vo{l}_n(K)vo{l}_n(K^{\ast })$ in the class of origin symmetric convex bodies endowed wit…