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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

A new proof of the Orlicz Busemann-Petty centroid inequality


Authors: Ai-Jun Li and Gangsong Leng
Journal: Proc. Amer. Math. Soc. 139 (2011), 1473-1481
MSC (2000): Primary 52A20, 52A40
Published electronically: September 30, 2010
MathSciNet review: 2748442
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Abstract: Using shadow systems, we provide a new proof of the Orlicz Busemann-Petty centroid inequality, which was first obtained by Lutwak, Yang and Zhang.


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Ai-Jun Li
Affiliation: Department of Mathematics, Shanghai University, Shanghai 200444, People’s Republic of China – and – School of Mathematics and Information Science, Henan Polytechnic University, Jiaozuo City, 454000, People’s Republic of China
Email: liaijun72@163.com

Gangsong Leng
Affiliation: Department of Mathematics, Shanghai University, Shanghai 200444, People’s Republic of China
Email: gleng@staff.shu.edu.cn

DOI: http://dx.doi.org/10.1090/S0002-9939-2010-10651-2
PII: S 0002-9939(2010)10651-2
Keywords: Orlicz centroid body, Orlicz Busemann-Petty centroid inequality, shadow system, parallel chord movement.
Received by editor(s): February 16, 2010
Received by editor(s) in revised form: April 27, 2010
Published electronically: September 30, 2010
Additional Notes: The authors would like to acknowledge the support from the National Natural Science Foundation of China (10971128), Shanghai Leading Academic Discipline Project (S30104), Scientific Research and Innovation Project of Shanghai Municipal Education Commission (09ZZ94) and Innovation Foundation of Shanghai University (SHUCX080134)
Communicated by: Mario Bonk
Article copyright: © Copyright 2010 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.