Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

   
Mobile Device Pairing
Green Open Access
Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Mixed projection inequalities


Author: Erwin Lutwak
Journal: Trans. Amer. Math. Soc. 287 (1985), 91-105
MSC: Primary 52A40
MathSciNet review: 766208
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: A number of sharp geometric inequalities for polars of mixed projection bodies (zonoids) are obtained. Among the inequalities derived is a polar projection inequality that has the projection inequality of Petty as a special case. Other special cases of this polar projection inequality are inequalities (between the volume of a convex body and that of the polar of its $ i$th projection body) that are strengthened forms of the classical inequalities between the volume of a convex body and its projection measures (Quermassintegrale). The relation between the Busemann-Petty centroid inequality and the Petty projection inequality is shown to be similar to the relation that exists between the Blaschke-Santaló inequality and the affine isoperimetric inequality of affine differential geometry. Some mixed integral inequalities are derived similar in spirit to inequalities obtained by Chakerian and others.


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


Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 52A40

Retrieve articles in all journals with MSC: 52A40


Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1985-0766208-7
PII: S 0002-9947(1985)0766208-7
Keywords: Centroid body, convex body, mixed area measure, mixed volume, projection body, projection measure (Quermassintegral), zonoid
Article copyright: © Copyright 1985 American Mathematical Society