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A stability result for p-centroid bodies
LuJun Guo,Gangsong Leng,Youjiang Lin 대한수학회 2018 대한수학회보 Vol.55 No.1
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.
ORIGIN-SYMMETRIC CONVEX BODIES WITH MINIMAL MAHLER VOLUME IN R2
Youjiang Lin,Gangsong Leng 대한수학회 2014 대한수학회보 Vol.51 No.1
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 R2 and of its polar body is minimal if and only if K is a parallelogram.
VOLUME INEQUALITIES FOR THE L p-SINE TRANSFORM OF ISOTROPIC MEASURES
LuJun Guo,Gangsong Leng 대한수학회 2015 대한수학회보 Vol.52 No.3
For p ≥ 1, sharp isoperimetric inequalities for the Lp-sine transform of isotropic measures are established. The corresponding reverse inequalities are obtained in an asymptotically optimal form. As applications of our main results, we present volume inequalities for convex bodies which are in Lp surface isotropic position.
PARALLEL SECTIONS HOMOTHETY BODIES WITH MINIMAL MAHLER VOLUME IN Rn
Youjiang Lin,Gangsong Leng 대한수학회 2014 대한수학회보 Vol.51 No.4
In the paper, we define a class of convex bodies in Rn–parallel sections homothety bodies, and for some special parallel sections homoth- ety bodies, we prove that n-cubes have the minimal Mahler volume.
PARALLEL SECTIONS HOMOTHETY BODIES WITH MINIMAL MAHLER VOLUME IN ℝ<sup>n</sup>
Lin, Youjiang,Leng, Gangsong Korean Mathematical Society 2014 대한수학회보 Vol.51 No.4
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.
A STABILITY RESULT FOR P-CENTROID BODIES
Guo, Lujun,Leng, Gangsong,Lin, Youjiang Korean Mathematical Society 2018 대한수학회보 Vol.55 No.1
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.
VOLUME INEQUALITIES FOR THE L<sub>p</sub>-SINE TRANSFORM OF ISOTROPIC MEASURES
Guo, LuJun,Leng, Gangsong Korean Mathematical Society 2015 대한수학회보 Vol.52 No.3
For $p{\geq}1$, sharp isoperimetric inequalities for the $L_p$-sine transform of isotropic measures are established. The corresponding reverse inequalities are obtained in an asymptotically optimal form. As applications of our main results, we present volume inequalities for convex bodies which are in $L_p$ surface isotropic position.
INEQUALITIES FOR DUAL HARMONIC QUERMASSINTEGRALS
Jun, Yuan,Shufeng Yuan,Gangsong Leng Korean Mathematical Society 2006 대한수학회지 Vol.43 No.3
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.
INEQUALITIES FOR STAR DUALS OF INTERSECTION BODIES
Jun, Yuan,Huawei, Zhu,Gangsong, Leng Korean Mathematical Society 2007 대한수학회지 Vol.44 No.2
In this paper, we present a new kind of duality between intersection bodies and projection bodies. Furthermore, we establish some counterparts of dual Brunn-Minkowski inequalities for intersection bodies.
ORIGIN-SYMMETRIC CONVEX BODIES WITH MINIMAL MAHLER VOLUME IN ℝ<sup>2</sup>
Lin, Youjiang,Leng, Gangsong Korean Mathematical Society 2014 대한수학회보 Vol.51 No.1
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.