• The $L_p$-Curvature Images of Convex Bodies and $L_p$-Projection Bodies

• # Fulltext

https://www.ias.ac.in/article/fulltext/pmsc/118/03/0413-0424

• # Keywords

𝑝-Curvature image; 𝑝-affine surface area; $L_p$-projection body; $L_p$-mixed volume; $L_p$-dual mixed volume.

• # Abstract

Associated with the $L_p$-curvature image defined by Lutwak, some inequalities for extended mixed 𝑝-affine surface areas of convex bodies and the support functions of $L_p$-projection bodies are established. As a natural extension of a result due to Lutwak, an $L_p$-type affine isoperimetric inequality, whose special cases are $L_p$-Busemann–Petty centroid inequality and $L_p$-affine projection inequality, respectively, is established. Some $L_p$-mixed volume inequalities involving $L_p$-projection bodies are also established.

• # Author Affiliations

1. College of Mathematics and Computer Science, Chongqing Normal University, Chongqing 400047, People’s Republic of China
2. Department of Mathematics, Shanghai University, Shanghai 200444, People’s Republic of China

• # Proceedings – Mathematical Sciences

Current Issue
Volume 129 | Issue 5
November 2019

• # Editorial Note on Continuous Article Publication

Posted on July 25, 2019