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The Petty Projection Inequality for L_p-Mixed Projection Bodies

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Acta Mathematica Sinica,English Series 2007年第8期23卷 1485-1494页

作者： Wei Dong WANG Gang Song LENG Department of Mathematics Hubei Institute for Nationalities Enshi 445000 P. R. China and Department of Mathematics Shanghai University Shanghai 200436 P. R. China E-mail: lenggangsong@***

Recently, Lutwak, Yang and Zhang posed the notion of lp-projection body and established the lp-analog of the Petty projection inequality. In this paper, the notion of lp-mixed projection body is introduced--the lp-projection body being a special case. The Petty projection inequality, as well as Lutwak＇s quermassintegrals （lp-mixed quermassintegrals） extension of the Petty projection inequality, is established for lp-mixed projection body.

关键词： petty projection inequality lp-projection body lp-mixed projection body lp-centroid body lp-mixed quermassintegrals

L_p-centroid Bodies and Its Characterizations

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Communications in Mathematical Research 2015年第4期31卷 333-344页

作者： Ma Tong-yi Zhang De-yan Rong Xiao-chun College of Mathematics and Statistics Hexi University

In this paper, we study the characteristic properties for lp-centroid bod- ies, and an improved version of Busemann-Petty problem for lp-centroid bodies is obtained. In addition, using the definitions of lp-pole curva... 详细信息

关键词： convex body star body centroid body lp-centroid body Busemann- Petty problem

On Reverses of the lp-petty Projection Inequality

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Chinese Quarterly Journal of Mathematics 2009年第4期24卷 491-498页

作者： WANG Wei-dong WEI Dai-jun XIANG Yu Department of Mathematics China Three Gorges University Yichang 443002 China Department of Mathematics Hubei Institute for Nationalities Enshi 445000 China

Lutwak, Yang and Zhang established the lp-petty projection inequality. In this paper, the several reverses of the lp-petty projection inequality are shown.

关键词： convex body lp-projection body lp-centroid body reverse lp-petty projection inequality

Busemann-Petty Type Problem for the General L_(p)-centroid Bodies

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Analysis in Theory and Applications 2023年第1期39卷 69-82页

作者： Weidong Wang Three Gorges Mathematical Research Center China Three Gorges UniversityYichangHubei 443002China College of Science China Three Gorges UniversityYichangHubei 443002China

Lutwak showed the Busemann-Petty type problem(also called the Shephard type problem)for the centroid *** and Zhang gave an affirmation and a negative form of the Busemann-Petty type problem for the L_(p)-centroid *** this paper,we obtain an affirmation form and two negative forms of the BusemannPetty type problem for the general L_(p)-centroid bodies.

关键词： lp-centroid body general L_(p)-centroid body Busemann-Petty problem affirmation form negation form