Differences of Quermass- and Dual Quermassintegrals of Blaschke-Minkowski and Radial Blaschke-Minkowski Homomorphisms

Abstract

In this article, we establish Minkowski, Brunn-Minkowski and Aleksandrov-Fenchel type inequalities for differences of quermass-and dual quermassintegrals of mixed Blaschke-Minkowski and mixed radial Blaschke-Minkowski homomorphisms.

Some inequalities for star duality of the radial Blaschke-Minkowski homomorphisms

“…Regarding the studies of the (mixed) radial Blaschke-Minkowski homomorphisms, many results have been found in the previous studies, see, e.g., [5][6][7][9][10][11][12][13][14][15][16][17][18]20].…”

Some inequalities for the (p,q)-mixed geominimal surface areas and Lp radial Blaschke-Minkowski homomorphisms

“…This gives inequality (6). In addition, equality holds in inequality (6) if and only if L 1 and L 2 are dilates.…”

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

“…From this, inequality Equation (25) is obtained. By the equality conditions of Equation (24) and the Minkowski integral inequality, we see that equality holds in Equation (25) if and only if K and L are dilated.…”

“…Meanwhile, associated with L p radial Blaschke-Minkowski homomorphisms, Wang et al [23] extended Schuster's results including the Busemann-Petty Problem 2. In recent years, a lot of important conclusions for the radial Blaschke-Minkowski homomorphisms and their L p analogies were obtained (see e.g., [22][23][24][25][26][27][28][29][30][31][32][33]).…”