• Journal of the Korean Mathematical Society
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• v.47 no.5
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• pp.935-945
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• 2010

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.

• Journal of the Korean Mathematical Society
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• v.37 no.6
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• pp.991-1005
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• 2000

We consider a zeta function of the classical dynamics in the exterior of several convex bodies. The main result is that the poles of the zeta function cannot converge to the line of absolute convergence if the abscissa of absolute convergence of the zeta function is positive.

• Bulletin of the Korean Mathematical Society
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• v.51 no.4
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• pp.1023-1029
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• 2014

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.

• Bulletin of the Korean Mathematical Society
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• v.51 no.1
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• pp.129-137
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• 2014

In this paper, a new proof of the following result is given: The product of the volumes of an origin-symmetric convex bodies K in $\mathbb{R}^2$ and of its polar body is minimal if and only if K is a parallelogram.

• 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.

• Communications of the Korean Mathematical Society
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• v.23 no.2
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• pp.241-250
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• 2008

In this article, we find a counter example which shows that the well-known necessary condition about the boundary regularity of a stable strictly convex body is not a sufficient condition.

• Bulletin of the Korean Mathematical Society
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• v.55 no.1
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• pp.139-148
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• 2018

In this paper, we prove a stability result for p-centroid bodies with respect to the Hausdorff distance. As its application, we show that the symmetric convex body is determined by its p-centroid body.

• 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.

• East Asian mathematical journal
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• v.16 no.2
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• pp.363-370
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• 2000

We evaluate the dual quermassintegrals of $\gamma$-equichordal bodies and obtain the lower bound for the volume product of p-centroid body in $E^2$.

• Bulletin of the Korean Mathematical Society
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• v.54 no.6
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• pp.2053-2063
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• 2017

In this paper we prove a condition under which a hyperbolic starshaped set has a center of hyperbolic symmetry. We also give the definition of isometric diameters for a hyperbolic convex set, which behave similar to affine diameters for Euclidean convex sets. Using this concept, we give a definition of constant hyperbolic width and we prove that the only hyperbolic sets with constant hyperbolic width and with a hyperbolic center of symmetry are hyperbolic discs.