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J. Korean Math. Soc. 2007; 44(6): 1373-1381

Printed November 1, 2007

Copyright © The Korean Mathematical Society.

An equivalence form of the Brunn-Minkowski inequality for volume differences

Chang-Jian Zhao and Wing-Sum Cheung

China Jiliang University, The University of Hong Kong

Abstract

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In this paper, we establish an equivalence form of the Brunn-Minkowski inequality for volume differences. As an application, we obtain a general and strengthened form of the dual Kneser-S\"{u}ss inequality.

Keywords: volume difference, convex body, star body, the Kneser-S\"uss inequality, the dual Kneser-S\"uss inequality, the Brunn-Minkowski inequality.

MSC numbers: Primary 52A40

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