关于Lp-极曲率映像的几个不等式

doi:10.13371/j.cnki.chin.q.j.m.2016.04.003

数学季刊 ›› 2016, Vol. 31 ›› Issue (4): 349-358.doi: 10.13371/j.cnki.chin.q.j.m.2016.04.003

关于L_p-极曲率映像的几个不等式

College of Mathematics and Statistics,Northwest Normal University. College of Mathematics and Statistics,Hexi University

收稿日期:2014-05-30 出版日期:2016-12-30 发布日期:2020-10-30
作者简介:LI Xin-hong(1986-), female, native of Lanzhou, Gansu, a postgradute of Northwest Normal University, engages in convex geometric analysis and geometric inequality theory; MA Tong-yi(1959-), male, native of Huining, Gansu, a professor of Hexi University, M.S.D., engages convex geometric analysis, distance geometry, discrete geometry and inequality theory.
基金资助:
Supported by the National Natural Science Foundation of China(11161019)；

Some Inequalities for the L_p-polar Curvature Images of Star Bodies

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College of Mathematics and Statistics,Northwest Normal University. College of Mathematics and Statistics,Hexi University

Received:2014-05-30 Online:2016-12-30 Published:2020-10-30
About author:LI Xin-hong(1986-), female, native of Lanzhou, Gansu, a postgradute of Northwest Normal University, engages in convex geometric analysis and geometric inequality theory; MA Tong-yi(1959-), male, native of Huining, Gansu, a professor of Hexi University, M.S.D., engages convex geometric analysis, distance geometry, discrete geometry and inequality theory.
Supported by:
Supported by the National Natural Science Foundation of China(11161019)；

摘要/Abstract

摘要： Zhu,Lü and Leng extended the concept of L_p-polar curvature image. We continuously study the L_p-polar curvature image and mainly expound the relations between the volumes of star bodies and their L_p-polar curvature images in this article. We first establish the L_p-affine isoperimetric inequality associated with L_p-polar curvature image. Secondly,we give a monotonic property for L_p-polar curvature image. Finally, we obtain an interesting equation related to L_p-projection body of L_p-polar curvature image and L_p-centroid body.

关键词: star bodies, convex bodies, L_p-curvature image, L_p-polar curvature image

Abstract: Zhu,Lü and Leng extended the concept of L_p-polar curvature image. We continuously study the L_p-polar curvature image and mainly expound the relations between the volumes of star bodies and their L_p-polar curvature images in this article. We first establish the L_p-affine isoperimetric inequality associated with L_p-polar curvature image. Secondly,we give a monotonic property for L_p-polar curvature image. Finally, we obtain an interesting equation related to L_p-projection body of L_p-polar curvature image and L_p-centroid body.

Key words: star bodies, convex bodies, L_p-curvature image, L_p-polar curvature image

中图分类号:

O178

李新红, 马统一. 关于L_p-极曲率映像的几个不等式[J]. 数学季刊, 2016, 31(4): 349-358.

LI Xin-hong, MA Tong-yi. Some Inequalities for the L_p-polar Curvature Images of Star Bodies[J]. Chinese Quarterly Journal of Mathematics, 2016, 31(4): 349-358.

[1]	魏波, 王卫东. 关于对偶均质积分的Dresher型不等式[J]. 数学季刊, 2015, 30(2): 199-205.
[2]	朱先阳. 关于Lp-混合仿射表面积的不等式[J]. 数学季刊, 2012, 27(4): 572-581.

关于L_p-极曲率映像的几个不等式

College of Mathematics and Statistics,Northwest Normal University. College of Mathematics and Statistics,Hexi University

Some Inequalities for the L_p-polar Curvature Images of Star Bodies

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关于Lp-极曲率映像的几个不等式

College of Mathematics and Statistics,Northwest Normal University. College of Mathematics and Statistics,Hexi University

Some Inequalities for the Lp-polar Curvature Images of Star Bodies

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关于L_p-极曲率映像的几个不等式

Some Inequalities for the L_p-polar Curvature Images of Star Bodies