The Busemann theorem for complex p-convex bodies

被引：0
作者：
Qingzhong Huang
Binwu He
Guangting Wang
机构：
[1] Shanghai University,Department of Mathematics
来源：
Archiv der Mathematik | 2012年 / 99卷
关键词：
52A20; -convex bodyss; Intersection body; Complex intersection body; Generalized radial ; th mean body; Busemann theorem;
D O I：
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学科分类号：
摘要：
The Busemann theorem states that the intersection body of an origin-symmetric convex body is also convex. In this paper, we prove a version of the Busemann theorem for complex p-convex bodies. Namely that the complex intersection body of an origin-symmetric complex p-convex body is γ-convex for certain γ. The result is the complex analogue of the work of Kim, Yaskin, and Zvavitch on (real) p-convex bodies. Furthermore, we show that the generalized radial qth mean body of a p-convex body is γ-convex for certain γ.
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页码：289 / 299
页数：10
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