The L p -dual mixed geominimal surface area for multiple star bodies

Yanan Li,Weidong Wang

doi:10.1186/1029-242x-2014-456

Abstract

According to the notion of the L p -mixed geominimal surface area of multiple convex bodies which were introduced by Ye et al., we define the concept of the L p -dual mixed geominimal surface area for multiple star bodies, and we establish several inequalities related to this concept.MSC:52A20, 52A40.

Highlights

Let Kn denote the set of convex bodies in Euclidean space Rn
For the set of convex bodies containing the origin in their interiors and the set of convex bodies whose centroids lie at the origin in Rn, we write Kon and Kcn, respectively
Son and Scn, respectively, denote the set of star bodies and the set of star bodies whose centroids lie at the origin in Rn

Summary

Introduction

Let Kn denote the set of convex bodies (compact, convex subsets with nonempty interiors) in Euclidean space Rn. For K ∈ Kon, and p ≥ , the Lp-geominimal surface area, Gp(K), of K is defined by p ωnn Gp(K ) = inf nVp(K , L)V Ye et al [ ] studied the Lp-mixed geominimal surface area for multiple convex bodies. For p > , they defined the Lp-mixed geominimal surface areas for K , .

Results

Conclusion