Volume Inequalities for Sections and Projections of Asymmetric Convex Bodies

CAO Zi-xin, Li Ai-jun

doi:10.13371/j.cnki.chin.q.j.m.2022.02.007

Chinese Quarterly Journal of Mathematics >

2022 , Vol. 37 >Issue 2: 178 - 188

DOI: https://doi.org/10.13371/j.cnki.chin.q.j.m.2022.02.007

Volume Inequalities for Sections and Projections of Asymmetric Convex Bodies

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1. School of Mathematics and Information Science, Henan Polytechnic University, Jiaozuo 454000, China; 2. School of Science, Zhejiang University of Science and Technology, Hangzhou 310023, China

CAO Zi-xin (1995-), famale, native of Xinyang, Henan, postgraduate student of Henan Polytechnic University, engages in convex geometrical analysis; Li Ai-jun (1972-), male, native of Jiaozuo, Henan, professor of Zhejiang University of Science and Technology, engages in convex geometrical analysis.

Received date: 2021-11-22

Online published: 2022-06-30

Supported by

The second author was supported by Zhejiang Provincial Natural Science Foundation of China (Grant No. LY22A010001).

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Abstract

In this paper, we establish volume inequalities for k-dimensional sections and projections of convex bodies (not necessarily symmetric) and their polars in a more general position than John’s position.

Key words： Section; Projection; Asymmetric; Brascamp-Lieb inequality

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CAO Zi-xin, Li Ai-jun . Volume Inequalities for Sections and Projections of Asymmetric Convex Bodies[J]. Chinese Quarterly Journal of Mathematics, 2022 , 37(2) : 178 -188 . DOI: 10.13371/j.cnki.chin.q.j.m.2022.02.007

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