Journal of the
Korean Mathematical Society
JKMS

ISSN(Print) 0304-9914 ISSN(Online) 2234-3008

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J. Korean Math. Soc. 2010; 47(5): 935-945

Printed September 1, 2010

https://doi.org/10.4134/JKMS.2010.47.5.935

Copyright © The Korean Mathematical Society.

Mixed brightness-integrals of convex bodies

Ni Li and Baocheng Zhu

Chongqing Normal University

Abstract

The mixed width-integrals of convex bodies are defined by E. Lutwak. In this paper, the mixed brightness-integrals of convex bodies are defined. An inequality is established for the mixed brightness-integrals analogous to the Fenchel-Aleksandrov inequality for the mixed volumes. An isoperimetric inequality (involving the mixed brightness-integrals) is presented which generalizes an inequality recently obtained by Chakerian and Heil. Strengthened version of this general inequality is obtained by introducing indexed mixed brightness-integrals.

Keywords: convex bodies, mixed projection bodies, brightness, mixed brightness, mixed brightness-integrals, Fenchel-Aleksandrov inequality

MSC numbers: 52A40

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