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

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

We prove that the unit cube B ∞ n 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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Veröffentlicht in:Duke mathematical journal 2010-09, Vol.154 (3), p.419-430
Hauptverfasser: Nazarov, Fedor, Petrov, Fedor, Ryabogin, Dmitry, Zvavitch, Artem
Format: Artikel
Sprache:eng
Schlagworte:
52A20
52A40
53C45
Convex sets in $n$ dimensions (including convex hypersurfaces) [See also 53A07
Inequalities and extremum problems
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Zusammenfassung:We prove that the unit cube B ∞ n 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.
ISSN:0012-7094
1547-7398
DOI:10.1215/00127094-2010-042