Lp-Dual Mixed Geominimal Surface Area

In this paper, a new Lp-dual mixed geominimal surface area is defined by Lp-dual mixed quermassintegrals, which extends the definition of Lp-dual geominimal surface area and generalizes some related inequalities established by Wan and Wang.

Some Inequalities for Geominimal Surface Areas

The concept of geominimal surface area is first intro- duced, and then, the affine surface area projection inequality is given by Petty. In recent years, associated with geominimal surface area, Lutwak obtained some significant results containing the extended affine projection inequality. In this paper, combining with curvature image and combinations of convex bodies, we get some inequalities for geominimal surface areas. Furthermore, the integral form of geominimal surface area is obtained.

The Shephard Type Problems for General L_p-Centroid Bodies

In this paper, combining with the L_p-dual geominimal surface area and the general L_p-centroid bodies, we research the Shephard type problems for general L_p-centroid bodies.

A Type of Shephard Problems for Lp Blaschke-Minkowski Homomorphisms

The Blaschke-Minkowski homomorphisms was defined by Schuster.Recently,Wang extended its concept to Lp version.In this paper,we obtain affirmative and negative forms of the Shephard type problems for Lp geominimal surface areas with respect to the Lp Blaschke-Minkowski homomorphisms.

A Type of Busemann-Petty Problems for Blaschke-Minkowski Homomorphisms

Schuster introduced the notion of Blaschke-Minkowski homomorphisms and first considered Busemann-Petty type problems. In this paper, we study the Busemann-Petty type problems for the geominimal surface area with respect to Blaschke-Minkowski homomorphisms.