Inequalities of Aleksandrov body

Abstract

Abstract A new concept of p-Aleksandrov body is firstly introduced. In this paper, p-Brunn-Minkowski inequality and p-Minkowski inequality on the p-Aleksandrov body are established. Furthermore, some pertinent results concerning the Aleksandrov body and the p-Aleksandrov body are presented. 2000 Mathematics Subject Classification: 52A20 52A40

Keywords

• Aleksandrov body
• <it>p-</it>Aleksandrov body
• Brunn-Minkowski inequality
• Minkowski inequality