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15 August 2014 From symplectic measurements to the Mahler conjecture
Shiri Artstein-Avidan, Roman Karasev, Yaron Ostrover
Duke Math. J. 163(11): 2003-2022 (15 August 2014). DOI: 10.1215/00127094-2794999

Abstract

In this note we link symplectic and convex geometry by relating two seemingly different open conjectures: a symplectic isoperimetric-type inequality for convex domains and Mahler’s conjecture on the volume product of centrally symmetric convex bodies. More precisely, we show that if for convex bodies of fixed volume in the classical phase space the Hofer–Zehnder capacity is maximized by the Euclidean ball, then a hypercube is a minimizer for the volume product among centrally symmetric convex bodies.

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Shiri Artstein-Avidan. Roman Karasev. Yaron Ostrover. "From symplectic measurements to the Mahler conjecture." Duke Math. J. 163 (11) 2003 - 2022, 15 August 2014. https://doi.org/10.1215/00127094-2794999

Information

Published: 15 August 2014
First available in Project Euclid: 8 August 2014

zbMATH: 1330.52004
MathSciNet: MR3263026
Digital Object Identifier: 10.1215/00127094-2794999

Subjects:
Primary: 52A20
Secondary: 37D50, 52A23, 52A40

Rights: Copyright © 2014 Duke University Press

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Vol.163 • No. 11 • 15 August 2014
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