• Journal of the Korean Mathematical Society
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• v.44 no.6
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• pp.1373-1381
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• 2007

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 $Kneser-S\ddot{u}ss$ inequality.

• Journal of the Korean Mathematical Society
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• v.43 no.3
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• pp.593-607
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• 2006

In this paper, we study the properties of the dual harmonic quermassintegrals systematically and establish some inequalities for the dual harmonic quermassintegrals, such as the Minkowski inequality, the Brunn-Minkowski inequality, the Blaschke-Santalo inequality and the Bieberbach inequality.

• Bulletin of the Korean Mathematical Society
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• v.52 no.2
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• pp.453-465
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• 2015

In this paper we establish general Minkowski inequality, Aleksandrov-Fenchel inequality and Brunn-Minkowski inequality for polars of mixed complex projection bodies.

• Journal of the Korean Mathematical Society
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• v.47 no.2
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• pp.277-288
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• 2010

The mixed chord-integrals are defined. The Fenchel-Aleksandrov inequality and a general isoperimetric inequality for the mixed chordintegrals are established. Furthermore, the dual general Bieberbach inequality is presented. As an application of the dual form, a Brunn-Minkowski type inequality for mixed intersection bodies is given.

• Journal of the Korean Mathematical Society
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• v.45 no.2
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• pp.587-596
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• 2008

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.