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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

A general isepiphanic inequality


Author: Erwin Lutwak
Journal: Proc. Amer. Math. Soc. 90 (1984), 415-421
MSC: Primary 52A40
MathSciNet review: 728360
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Abstract: An inequality of Petty regarding the volume of a convex body and that of the polar of its projection body is shown to lead to an inequality between the volume of a convex body and the power means of its brightness function. A special case of this power-mean inequality is the classical isepiphanic (isoperimetric) inequality. The power-mean inequality can also be used to obtain strengthened forms and extensions of some known and conjectured geometric inequalities. Affine projection measures (Quermassintegrale) are introduced.


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DOI: https://doi.org/10.1090/S0002-9939-1984-0728360-3
Keywords: Convex body, projection body, projection measure (Quermassintegrale)
Article copyright: © Copyright 1984 American Mathematical Society