The Extrema of \(q\)- and Dual \(q\)-Quermassintegrals for the Asymmetric \(L_p\)-Difference Bodies

Abstract

Wang and Ma introduced the notion of asymmetric \(L_p\)-difference bodies. They further gave the extrema of volumes for the asymmetric \(L_p\)-difference body and its polar. Thereafter, Shi and Wang obtained their versions of quermassintegrals and dual quermassintegrals. In this paper, we determine the extrema of the \(q\)-quermassintegrals and dual \(q\)-quermassintegrals for the asymmetric \(L_p\)-difference bodies.