Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
   
Mobile Device Pairing
Green Open Access
Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Cross $ i$-sections of star bodies and dual mixed volumes


Authors: Songjun Lv and Gangsong Leng
Journal: Proc. Amer. Math. Soc. 135 (2007), 3367-3373
MSC (2000): Primary 52A30, 52A40
Published electronically: June 20, 2007
MathSciNet review: 2322769
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: In this paper, we establish an extension of Funk's section theorem. Our result has the following corollary: If $ K$ is a star body in $ \mathbb{R}^n$ whose central $ i$-slices have the same volume (with appropriate dimension) as the central $ i$-slices of a centered body $ M$, then the dual quermassintegrals satisfy $ \widetilde{W}_j(M)\leq \widetilde{W}_j(K)$, for any $ 0\leq j<n-i$, with equality if and only if $ K=M$. The case that $ K$ is a centered body implies Funk's section theorem.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 52A30, 52A40

Retrieve articles in all journals with MSC (2000): 52A30, 52A40


Additional Information

Songjun Lv
Affiliation: Department of Mathematics, Shanghai University, Shanghai, People’s Republic of China 200444
Email: lvsongjun@126.com

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

DOI: http://dx.doi.org/10.1090/S0002-9939-07-08997-6
PII: S 0002-9939(07)08997-6
Keywords: Star body, cross $i$-section, dual mixed volume, Radon transform
Received by editor(s): June 19, 2006
Published electronically: June 20, 2007
Additional Notes: This research was supported, in part, by NSFC Grant 10671117.
Communicated by: Jonathan M. Borwein
Article copyright: © Copyright 2007 American Mathematical Society