Orlicz geominimal surface areas

Abstract

In 1996, E. Lutwak extended the important concept of geominimal surface area to L p version, which serves as a bridge connecting a number of areas of geometry: affine differential geometry, relative differential geometry, and Minkowskian geometry. In this paper, by using the concept of Orlicz mixed volume, we extend geominimal surface area to the Orlicz version and give some properties and an isoperimetric inequalities for the Orlicz geominimal surface areas.