Lp-dual three mixed quermassintegrals

Abstract

In the paper, the concept of Lp-dual three-mixed quermassintegrals is introduced. The formula for the Lp-dual three-mixed quermassintegrals with respect to the p-radial addition is proved. Inequalities of Lp-Minkowski, and Brunn-Minkowski type for the Lp-dual three-mixed quermassintegrals are established. The new Lp-Minkowski inequality is obtained that generalize a family of Minkowski type inequalities. The Lp-Brunn-Minkowski inequality is used to obtain a series of Brunn-Minkowski type inequalities.

Keywords

• p-radial addtion
• dual quermassintegral
• dual mixed quermassintegral
• minkowski inequality
• brunn-minkowski inequality
• primary 52a40
• secondary 46e30