On mixed complex intersection bodies

Abstract

Abstract. Complex intersection bodies were introduced by Koldobsky, Paouris and Zymonopoulou. In this paper some geometric inequalities for mixed complex intersection bodies which are dual forms of inequalities for mixed complex projection bodies are established.Mathematics subject classification (2010): 52A40, 52A20.

On mixed complex intersection bodies

“…This is just a new result established by Wang et al [24]. On the other hand, taking for r = 2n − 2, (3.6), it becomes to the following result.…”

“…In exactly the same way, it can be seen that with equality if and only if K and L are dilates. This is just a new inequality established by Wang et al [24].…”

“…In 2015, Wang et al [24] established Minkowski inequality and Brunn-Minkowski inequality for the mixed complex intersection bodies, respectively. Theorem 1.1.…”

Dual mixed complex brightness integrals

“…In particular, by I C B = ω 2n−2 π B (see page 1642 of [36]), since for every ξ ∈ S 2n−1 , by (2), Wang et.al. (see page 422 of [30]) obtained…”

“…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]).…”