On Blaschke-Minkowski homomorphisms

Abstract

In this article we establish a Brunn-Minkowski-type inequality for mixed Blaschke-Minkowski homomorphisms.

On p-radial Blaschke and harmonic Blaschke additions

“…Radial Blaschke-Minkowski homomorphisms are important examples of star body valued valuations. Their natural duals, Blaschke-Minkowski homomorphisms, are an important notion in the theory of convex body valued valuations (see, e.g., [ 6 – 12 ] and [ 13 – 20 ]). In 2006, Schuster [ 5 ] established the following Brunn-Minkowski inequality for radial Blaschke-Minkowski homomorphisms of star bodies.…”

On radial and polar Blaschke-Minkowski homomorphisms

“…Blaschke-Minkowski homomorphisms are an important notion in the theory of convex body-valued valuations (see, e.g., [5]- [6], [9]- [10], [15], [19], [22] and [1]- [2], [7]- [8], [11]- [12], [20]- [21]). They are natural duals to radial Blaschke-Minkowski homomorphisms which are important examples of star body-valued valuations.…”

On polars of Blaschke-Minkowski homomorphisms

“…Blaschke-Minkowski homomorphism is an important notion in the theory of convex body valued valuations (see, e.g., [1], [5], [8], [10], [12]- [14], [17], [21], [23]- [25], [30]). Their natural dual, radial Blaschke-Minkowski homomorphism, was introduced by Schuster [20] and further investigated to be meaningful (see [22]).…”