Taiwanese Journal of Mathematics

A GENERAL $L_p$-VERSION OF PETTY'S AFFINE PROJECTION INEQUALITY

Weidong Wang and Yibin Feng

Full-text: Open access

Abstract

About a decade ago Lutwak, Yang, and Zhang introduced the notion of $L_p$-projection body. More recently, Wang and Leng established an $L_p$-version of Petty's affine projection inequality. At the same time Ludwig discovered a family of general $L_p$-projection bodies and Haberl and Schuster established Petty's projection inequality for general $L_p$-projection bodies. In this paper we establish a general $L_p$-version of Petty's affine projection inequality for general $L_p$-projection bodies. Moreover, we obtain an analogous inequality for $L_p$-geominimal surface area.

Article information

Source
Taiwanese J. Math., Volume 17, Number 2 (2013), 517-528.

Dates
First available in Project Euclid: 10 July 2017

Permanent link to this document
https://projecteuclid.org/euclid.twjm/1499705951

Digital Object Identifier
doi:10.11650/tjm.17.2013.2122

Mathematical Reviews number (MathSciNet)
MR3044520

Zentralblatt MATH identifier
1283.52008

Subjects
Primary: 52A40: Inequalities and extremum problems 52A20: Convex sets in n dimensions (including convex hypersurfaces) [See also 53A07, 53C45]

Keywords
general $L_p$-projection body $L_p$-Petty affine projection inequality $L_p$-Affine surface area $L_p$-Geominimal surface area

Citation

Wang, Weidong; Feng, Yibin. A GENERAL $L_p$-VERSION OF PETTY'S AFFINE PROJECTION INEQUALITY. Taiwanese J. Math. 17 (2013), no. 2, 517--528. doi:10.11650/tjm.17.2013.2122. https://projecteuclid.org/euclid.twjm/1499705951


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