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 Parallel sections homothety bodies with minimal Mahler volume in $\mathbb{R}^n$ Bull. Korean Math. Soc. 2014 Vol. 51, No. 4, 1023-1029 https://doi.org/10.4134/BKMS.2014.51.4.1023Printed July 1, 2014 Youjiang Lin and Gangsong Leng Shanghai University, Shanghai University Abstract : In the paper, we define a class of convex bodies in $\mathbb{R}^n$--parallel sections homothety bodies, and for some special parallel sections homothety bodies, we prove that $n$-cubes have the minimal Mahler volume. Keywords : convex body, polar body, parallel sections homothety bodies, Mahler conjecture, cylinder MSC numbers : 52A10, 52A40 Downloads: Full-text PDF