Complex affine isoperimetric inequalities

Dual mixed complex brightness integrals

“…Until recently, the situation with complex convex bodies began to attract attention (see [2, 4, 12-15, 17, 26, 42, 43]). Some classical concepts of convex geometry in real vector space were extended to complex cases, such as complex projection bodies (see [3,20,29,39]), complex difference bodies (see [1]), complex intersection bodies (see [16,30,36,40]), complex centroid bodies (see [10,19]) and mixed complex brightness integrals (see [18]).…”

Inequalities on ComplexLpCentroid Bodies

“…Harberl [29] firstly proposed the complex centroid body of K and established the Busemann-Petty centroid inequality. In 2021, Wu [30] introduced the concept of the…”