Further inequalities and properties of p-inner parallel bodies. (9th April 2022)

• Record Type: Journal Article
• Authors: Lou, Yingying; Xi, Dongmeng; Zeng, Zhenbing
• Is Part Of: Canadian journal of mathematics. Volume 74:Number 2(2022)
• Page Start: 368
• Page End: 380
• Publication Date: 2022-04-09
• Subjects: 52A20 -- 52A39 -- 52A40; p-Inner parallel body -- 0-extreme normal vector -- tangential body; Mathematics -- Periodicals; Mathematics; Electronic journals; Periodicals; 510
• DOI: 10.4153/S0008414X20000796
• Languages: English
• ISSNs: 0008-414X

Abstract

Abstract: A. R. Martínez Fernández obtained upper bounds for quermassintegrals of the p -inner parallel bodies: an extension of the classical inner parallel body to the $L_p$ -Brunn-Minkowski theory. In this paper, we establish (sharp) upper and lower bounds for quermassintegrals of p -inner parallel bodies. Moreover, the sufficient and necessary conditions of the equality case for the main inequality are obtained, which characterize the so-called tangential bodies.