Bulletin of the
Korean Mathematical Society BKMS

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Bull. Korean Math. Soc. 2014; 51(4): 1023-1029

Printed July 1, 2014

https://doi.org/10.4134/BKMS.2014.51.4.1023

Copyright © The Korean Mathematical Society.

Parallel sections homothety bodies with minimal Mahler volume in $\mathbb{R}^n$

Youjiang Lin and Gangsong Leng

Shanghai University, Shanghai University

Abstract

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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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