Origin-symmetric convex bodies with minimal Mahler volume in $\mathbb{R}^2$
Bull. Korean Math. Soc. 2014 Vol. 51, No. 1, 129-137
Printed January 1, 2014
Youjiang Lin and Gangsong Leng
Shanghai University, Shanghai University
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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