Isoperimetric and Brunn-Minkowski inequalities for the (p, q)-mixed geominimal surface areas

Abstract

Motivated by the celebrated work of Lutwak, Yang and Zhang [1] on (p,q)\left(p,q)-mixed volumes and that of Feng and He [2] on (p,q)\left(p,q)-mixed geominimal surface areas, we in the present paper establish and confirm the affine isoperimetric and Brunn-Minkowski-type inequalities with respect to (p,q)\left(p,q)-mixed geominimal surface areas.

Keywords

• (p, q)-mixed volume
• (p, q)-mixed geominimal surface area
• monotonic inequality
• isoperimetric inequality
• brunn-minkowski-type inequality
• 52a20
• 52a39
• 52a40