Alexandrov-Fenchel type inequalities in the sphere

A Form of Alexandrov - Fenchel Inequalitypengfei Guan

Lp-Minkowski and Aleksandrov-Fenchel type inequalities

In this paper we establish the Lp-Minkowski inequality and Lp-Aleksandrov-Fenchel type inequality for Lp-dual mixed volumes of star duality of mixed intersection bodies, respectively. As applications, we get some related results. The paper new contributions that illustrate this duality of projection and intersection bodies will be presented. M.S.C. 2000: 52A40.

The Aleksandrov-Fenchel type inequalities for volume differences

In this paper we establish the Aleksandrov-Fenchel type inequality for volume differences function of convex bodies and the Aleksandrov-Fenchel inequality for Quermassintegral differences of mixed projection bodies, respectively. As applications, we give positive solutions of two open problems. M.S.C. 2000: 52A40.

Hardy type inequalities on the sphere

In this paper, we consider the [Formula: see text]-Hardy inequalities on the sphere. By the divergence theorem, we establish the [Formula: see text]-Hardy inequalities on the sphere. Furthermore, we also obtain their best constants. Our results can be regarded as the extension of Xiao's (J. Math. Inequal. 10:793-805, 2016).

On a relative Alexandrov-Fenchel inequality for convex bodies in Euclidean spaces

In this note we prove a localized form of Alexandrov-Fenchel inequality for convex bodies, i.e. we prove a class of isoperimetric inequalities in a ball involving Federer curvature measures. 1991 Mathematics Subject Classification: 52A20, 52A39, 52A40, 49Q15.