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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

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

Inequalities relating to L_p-version of Petty's conjectured projection inequality

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Applied Mathematics and Mechanics(English Edition) 2007年第2期28卷 269-276页

作者：王卫东冷岗松 Department of Mathematics Shanghai University

Petty＇s conjectured projection inequality is a famous open problem in the theory of convex bodies. In this paper, it is shown that an inequality relating to lp-version of the Petty＇s conjectured projection inequality is developed by using the notions of the lp-mixed volume and the lp-dual mixed volume, the relation of the lp-projection body and the geometric body Г-pK, the Bourgain-Milman inequality and the lp-Bnsemann-Petty inequality. In addition, for each origin-symmetric convex body, by applying the Jensen inequality and the monotonicity of the geometric body Г-pK, the reverses of lp-version of the Petty＇s conjectured projection inequality and the lp-Petty projection inequality are given, respectively.

关键词： lp-version Petty projection inequality Petty's conjectured projectioninequality lp-projection body reverse