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

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

2009-05-06

arxiv.org/abs/0905.0867v1

Mathematics

Functional Analysis

Scientific paper

We prove that the unit cube $B^n_{\infty}$ is a strict local minimizer for
the Mahler volume product $vol_n(K)vol_n(K^*)$ in the class of origin symmetric
convex bodies endowed with the Banach-Mazur distance.

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