Lp Radial Blaschke-Minkowski Homomorphisms and Lp Dual Affine Surface Areas

On Lp-affine surface areas

Let K be a convex body in Rn with centroid at 0 and B be the Euclidean unit ball in Rn centered at 0. We show that limt→0 |K| − |Kt| |B| − |Bt| = Op(K) Op(B) , where |K| respectively |B| denotes the volume of K respectively B, Op(K) respectively Op(B) is the p-affine surface area of K respectively B and {Kt}t≥0, {Bt}t≥0 are general families of convex bodies constructed from K, B satisfying cert...

DUAL Lp AFFINE ISOPERIMETRIC INEQUALITIES

Corresponding to each convex (or more general) subset of n-dimensional Euclidean space, Rn, there is a unique ellipsoid with the following property. The moment of inertia of the ellipsoid and the moment of inertia of the convex set are the same about every 1-dimensional subspace of Rn. This ellipsoid is called the Legendre ellipsoid of the convex set. The Legendre ellipsoid is a well-known conc...

Lp-dual geominimal surface areas for the general Lp-intersection bodies

For 0 < p < 1, Haberl and Ludwig defined the notions of symmetric and asymmetric Lp-intersection bodies. Recently, Wang and Li introduced the general Lp-intersection bodies. In this paper, we give the Lp-dual geominimal surface area forms for the extremum values and Brunn-Minkowski type inequality of general Lp-intersection bodies. Further, combining with the Lp-dual geominimal surface areas, w...

Lp-Dual geominimal surface area

* Correspondence: [email protected] Department of Mathematics, China Three Gorges University, Yichang, 443002, China, Abstract Lutwak proposed the notion of Lp-geominimal surface area according to the Lpmixed volume. In this article, associated with the Lp-dual mixed volume, we introduce the Lp-dual geominimal surface area and prove some inequalities for this notion. 2000 Mathematics Subject Cla...

AN Lp DEFINITION OF INTERPOLATING BLASCHKE PRODUCTS