Lp mixed geominimal surface area

This paper deals with Lp geominimal surface area and its extension to Lp mixed geominimal surface area. We give an integral formula of Lp geominimal surface area by the p-Petty body and introduce the concept of Lp mixed geominimal surface area which is a natural extension of Lp geominimal surface area. Some inequalities, such as, analogues of Alexandrov-Fenchel inequalities, Blaschke-Santaló inequalities, and affine isoperimetric inequalities for Lp mixed geominimal surface areas are obtained.