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)

 

A geometric inequality and a low $M$-estimate


Author: Bo'az Klartag
Journal: Proc. Amer. Math. Soc. 132 (2004), 2619-2628
MSC (2000): Primary 46B20, 52A20, 52A40
Published electronically: April 21, 2004
MathSciNet review: 2054787
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: We present an integral inequality connecting volumes and diameters of sections of a convex body. We apply this inequality to obtain some new inequalities concerning diameters of sections of convex bodies, among which is our ``low $M$-estimate''. Also, we give novel, alternative proofs to some known results, such as the fact that a finite volume ratio body has proportional sections that are isomorphic to a Euclidean ball.


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


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 46B20, 52A20, 52A40

Retrieve articles in all journals with MSC (2000): 46B20, 52A20, 52A40


Additional Information

Bo'az Klartag
Affiliation: School of Mathematical Sciences, Tel-Aviv University, Tel-Aviv 69978, Israel
Email: klartagb@post.tau.ac.il

DOI: http://dx.doi.org/10.1090/S0002-9939-04-07484-2
PII: S 0002-9939(04)07484-2
Keywords: Asymptotic geometric analysis, diameters of sections
Received by editor(s): May 26, 2003
Published electronically: April 21, 2004
Additional Notes: This research was partially supported by the Israel Science Foundation and by the Minkowski Center for Geometry
Communicated by: N. Tomczak-Jaegermann
Article copyright: © Copyright 2004 American Mathematical Society