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.2014.51.4.1023
Published online 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
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