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

By Fedor Nazarov, F. Petrov, D. Ryabogin, Artem Zvavitch. 2009

68 citations recorded by the source corpus.

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.

Subfields: Applied Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/88e1791f95decc19c8f59f359688783fee2aeb58

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

1. Roman N. Karasev
2. Y. Ostrover
3. Shiri Artstein-Avidan
4. Sergey G. Bobkov
5. V. Milman

In Geometry and Topology

1. Y. Ostrover
2. Shiri Artstein-Avidan
3. Roman N. Karasev
4. R. Leclercq
5. Yong-Geun Oh
6. Michael Entov
7. L. Polterovich

Citations in the corpus

• R\'enyi Divergence and $L_p$-affine surface area for convex bodies (2011, unknown): “, [5], [7] - [11], [13], [14], [17] - [24], [26], [28], [31] - [34], [37], [38] - [46], [50]), is now a central part of modern convex geometry.”
• Shadow systems of asymmetric Lp zonotopes (2013, unknown): “[1,3,6,7,10,13,18–20,31,33,34,38,39,41]).”
• From symplectic measurements to the Mahler conjecture (2013, background): “In higher dimensions it is proved only in some very special cases, namely, when the unit ball of X is a zonoid [9, 24], when X has a 1-unconditional basis [20, 26, 25], and when the unit ball of X is sufficiently close to the unit cube in the Banach–Mazur distance [22].”