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http://dx.doi.org/10.4134/JKMS.2008.45.2.587

INEQUALITIES FOR CHORD POWER INTEGRALS  

Xiong, Ge (DEPARTMENT OF MATHEMATICS SHANGHAI UNIVERSITY)
Song, Xiaogang (DEPARTMENT OF MATHEMATICS SHANGHAI UNIVERSITY)
Publication Information
Journal of the Korean Mathematical Society / v.45, no.2, 2008 , pp. 587-596 More about this Journal
Abstract
For convex bodies, chord power integrals were introduced and studied in several papers (see [3], [6], [14], [15], etc.). The aim of this article is to study them further, that is, we establish the Brunn-Minkowski-type inequalities and get the upper bound for chord power integrals of convex bodies. Finally, we get the famous Zhang projection inequality as a corollary. Here, it is deserved to mention that we make use of a completely distinct method, that is using the theory of inclusion measure, to establish the inequality.
Keywords
convex body; chord power integrals; inclusion measure;
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