The (p, q)-mixed geominimal surface areas

Abstract

The (p, q)-mixed geominimal surface areas are introduced. A special case of the new concept is the L_p geominimal surface area introduced by Lutwak. Related inequalities, such as affine isoperimetric inequality, monotonous inequality, cyclic inequality, and Brunn-Minkowski inequality, are established. These new inequalities strengthen some well-known inequalities related to the L_p geominimal surface area.