关于Lp-混合仿射表面积的不等式

数学季刊 ›› 2012, Vol. 27 ›› Issue (4): 572-581.

关于Lp-混合仿射表面积的不等式

Department of Mathematics, Jinggangshan University

收稿日期:2011-04-19 出版日期:2012-12-30 发布日期:2023-03-16
作者简介:ZHU Xian-yang(1969-), male, native of Xiangtan, Hunan, an associate professor of Jinggangshan University, Ph.D., engages in convex geometry analysis.
基金资助:
Supported by the NNSF of China(11161024)； Supported by the NSF of Jiangxi Province (2010GZC0115)

Some Inequalities for Lp-mixed Affne Surface Area

Department of Mathematics, Jinggangshan University

Received:2011-04-19 Online:2012-12-30 Published:2023-03-16
About author:ZHU Xian-yang(1969-), male, native of Xiangtan, Hunan, an associate professor of Jinggangshan University, Ph.D., engages in convex geometry analysis.
Supported by:
Supported by the NNSF of China(11161024)； Supported by the NSF of Jiangxi Province (2010GZC0115)

摘要/Abstract

摘要： In this paper, the concepts of the ith L_p-mixed affine surface area and L_p-polar curvature images are introduced, some new inequalities connecting these new notions with L_p-centroid bodies and p-Blaschke bodies are showed. Moreover, a Blaschke-Santaio type inequality for L_p-mixed affine surface area is established. Our results also imply the similar to the inequalities for Marcus-Lopes, Bergstrom and Ky Fan.

关键词: L_p-mixed affine surface area, L_p-polar curvature images, p-Blaschke linear combination, L_p-centroid body

Abstract: In this paper, the concepts of the ith L_p-mixed affine surface area and L_p-polar curvature images are introduced, some new inequalities connecting these new notions with L_p-centroid bodies and p-Blaschke bodies are showed. Moreover, a Blaschke-Santaio type inequality for L_p-mixed affine surface area is established. Our results also imply the similar to the inequalities for Marcus-Lopes, Bergstrom and Ky Fan.

Key words: L_p-mixed affine surface area, L_p-polar curvature images, p-Blaschke linear combination, L_p-centroid body

中图分类号:

O184

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.

ZHU Xian-yang. Some Inequalities for Lp-mixed Affne Surface Area[J]. Chinese Quarterly Journal of Mathematics, 2012, 27(4): 572-581.