关于Lp-极投影体Shephard问题的一个类似

doi:10.13371/j.cnki.chin.q.j.m.2015.04.013

数学季刊 ›› 2015, Vol. 30 ›› Issue (4): 596-609.doi: 10.13371/j.cnki.chin.q.j.m.2015.04.013

关于L_p-极投影体Shephard问题的一个类似

College of Mathematics and Statistics, Hexi University

收稿日期:2014-03-21 出版日期:2015-12-30 发布日期:2020-11-19
作者简介:MA Tong-yi(1959-), male, Huining, Gansu, a professor of Hexi University, engages in convex geometric analysis and distance geometry study.
基金资助:
Supported by the National Natural Science Foundation of China(11561020,11371224)； Supported by the Science and Technology Plan of the Gansu Province(145RJZG227)；

On the Analog of Shephard Problem for L_p-polar Projection Bodies

College of Mathematics and Statistics, Hexi University

Received:2014-03-21 Online:2015-12-30 Published:2020-11-19
About author:MA Tong-yi(1959-), male, Huining, Gansu, a professor of Hexi University, engages in convex geometric analysis and distance geometry study.
Supported by:
Supported by the National Natural Science Foundation of China(11561020,11371224)； Supported by the Science and Technology Plan of the Gansu Province(145RJZG227)；

摘要/Abstract

摘要： For p > 0, Lutwak, Yang and Zhang introduced the concept of L_p-polar projection body Γ_-pK of a convex body K in Rⁿ. Let p ≥ 1 and K, L \subset Rⁿbe two origin-symmetric convex bodies, we consider the question of whether Γ_-p K \subset Γ_-p L implies \Omega_p（L） ≤ \Omega_p（K）,where \Omega_p（K） denotes the L_p-affine surface area of K and K = Voln（K）^-1/pK. We prove a necessary and sufficient condition of an analog of the Shephard problem for the L_p-polar projection bodies.

关键词: convex body, L_p-polar projection body, L_p-affine surface area, Fourier transform, Shephard problem

Abstract: For p > 0, Lutwak, Yang and Zhang introduced the concept of L_p-polar projection body Γ_-pK of a convex body K in Rⁿ. Let p ≥ 1 and K, L \subset Rⁿbe two origin-symmetric convex bodies, we consider the question of whether Γ_-p K \subset Γ_-p L implies \Omega_p（L） ≤ \Omega_p（K）,where \Omega_p（K） denotes the L_p-affine surface area of K and K = Voln（K）^-1/pK. We prove a necessary and sufficient condition of an analog of the Shephard problem for the L_p-polar projection bodies.

Key words: convex body, L_p-polar projection body, L_p-affine surface area, Fourier transform, Shephard problem

中图分类号:

O186.5

马统一. 关于L_p-极投影体Shephard问题的一个类似[J]. 数学季刊, 2015, 30(4): 596-609.

MA Tong-yi. On the Analog of Shephard Problem for L_p-polar Projection Bodies[J]. Chinese Quarterly Journal of Mathematics, 2015, 30(4): 596-609.

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关于L_p-极投影体Shephard问题的一个类似

On the Analog of Shephard Problem for L_p-polar Projection Bodies

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关于Lp-极投影体Shephard问题的一个类似

On the Analog of Shephard Problem for Lp-polar Projection Bodies

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关于L_p-极投影体Shephard问题的一个类似

On the Analog of Shephard Problem for L_p-polar Projection Bodies