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.

Abstract. In this paper, we first introduce a new concept -radial p -th moment of a random vector for star body, which is a general form of the standard p -th moment. Further we establish some properties of the radial p -th moment and give some related applications.Mathematics subject classification (2010): 94A17, 60D05, 52A40.

Complex projection bodies were introduced by Abardia and Bernig, recently. In this paper some geometric inequalities for mixed complex projection bodies which are analogs of inequalities for mixed real projection bodies are established.

In this paper, we establish functional forms of the Orlicz Brunn-Minkowski inequality and the Orlicz-Minkowski inequality for the electrostatic q-capacity, which generalize previous results by Zou and Xiong. We also show that these two inequalities are equivalent.

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