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 Origin-symmetric convex bodies with minimal Mahler volume in $\mathbb{R}^2$ Bull. Korean Math. Soc. 2014 Vol. 51, No. 1, 129-137 https://doi.org/10.4134/BKMS.2014.51.1.129Printed 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 Downloads: Full-text PDF