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arXiv · 0905.0867

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

Fedor Nazarov·Fedor Petrov·Dmitry Ryabogin·Artem Zvavitch
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Abstract

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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Fedor Nazarov, Fedor Petrov, Dmitry Ryabogin, Artem Zvavitch. 2009-05-06. A remark on the Mahler conjecture: local minimality of the unit cube. https://doi.org/10.1215/00127094-2010-042

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