Acta mathematica scientia,Series A ›› 2012, Vol. 32 ›› Issue (4): 753-767.

• Articles • Previous Articles     Next Articles

On Lp-Intersection Body and Lp-Mixed Intersection Body

 MA Tong-Yi   

  1. College of Mathematics and Statistics, Hexi University, Gansu Zhangye 734000
  • Received:2011-05-29 Revised:2012-04-27 Online:2012-08-25 Published:2012-08-25
  • Supported by:

    国家自然科学基金(11161019)和甘肃省教育厅研究生导师科研基金(1009B-09)资助

Abstract:

For p<1and p≠0, Haberl and Ludwig introduced an Lp-intersection body IpK of a star body K. In this paper we study extreme nature of the
Lp-intersection body, and Lp-type Busemann-Petty intersection inequality is established. Meanwhile, we further expand the concept of 
Lp-intersection body to Lp-mixed intersection body is put forward. As an application, we  establish Aleksandrov-Fenchel type inequalities for Lp-mixed intersection body and its polar body. These results are the dual form of some known results.

Key words: Intersection body, Lp-intersection body, Lp-mixed intersection body

CLC Number: 

  • 52A40
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