Origin-symmetric convex bodies with minimal Mahler volume in $\mathbb{R}^2$

Youjiang Lin; Gangsong Leng

doi:10.4134/BKMS.2014.51.1.129

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Bull. Korean Math. Soc. 2014; 51(1): 129-137

Printed January 1, 2014

https://doi.org/10.4134/BKMS.2014.51.1.129

Origin-symmetric convex bodies with minimal Mahler volume in $\mathbb{R}^2$

Youjiang Lin and Gangsong Leng

Shanghai University, Shanghai University

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Abstract

In this paper, a new proof of the following result is given: The product of the volumes of an origin-symmetric convex bodies $K$ in $\mathbb{R}^2$ and of its polar body is minimal if and only if $K$ is a parallelogram.

Keywords: convex body, polar body, Mahler conjecture, polytopes

MSC numbers: 52A10, 52A40

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Origin-symmetric convex bodies with minimal Mahler volume in $\mathbb{R}^2$

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Origin-symmetric convex bodies with minimal Mahler volume in $\mathbb{R}^2$

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Article Tools

Stats or Metrics

Share this article on :

Related articles in BKMS

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Bulletin of the
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