由相交体确定凸体的稳定性

马统一

doi:10.13371/j.cnki.chin.q.j.m.2017.02.010

数学季刊 >

2017 , Vol. 32 >Issue 2: 194 - 207

DOI: https://doi.org/10.13371/j.cnki.chin.q.j.m.2017.02.010

由相交体确定凸体的稳定性

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College of Mathematics and Statistics, Hexi University

MA Tong-yi(1959-), male, native of Huining, Gansu, a professor of Hexi University, engages in convex geometric analysis and distance geometry study.

收稿日期: 2015-03-21

网络出版日期: 2020-10-23

基金资助

Supported by the National Natural Science Foundation of China(11561020,11371224)；

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Stable Determination of Convex Bodies from Intersection Bodies

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College of Mathematics and Statistics, Hexi University

MA Tong-yi(1959-), male, native of Huining, Gansu, a professor of Hexi University, engages in convex geometric analysis and distance geometry study.

Received date: 2015-03-21

Online published: 2020-10-23

Supported by

Supported by the National Natural Science Foundation of China(11561020,11371224)；

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摘要

In this paper, by means of the dual Brunn-Minkowski theories and methods as well as the integral transform, we have established a stability version of nonsymmetric convex bodies from intersection bodies. In addition, a stability results of symmetric convex bodies from Lp-counterparts is established.

关键词： convex body; intersection body; Lp-intersection body; spherical Radon transform; stability

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马统一 . 由相交体确定凸体的稳定性[J]. 数学季刊, 2017 , 32(2) : 194 -207 . DOI: 10.13371/j.cnki.chin.q.j.m.2017.02.010

Abstract

Key words： convex body; intersection body; Lp-intersection body; spherical Radon transform; stability

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