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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

Volume of mixed bodies


Author: Erwin Lutwak
Journal: Trans. Amer. Math. Soc. 294 (1986), 487-500
MSC: Primary 52A40; Secondary 52A22
MathSciNet review: 825717
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Abstract: By using inequalities obtained for the volume of mixed bodies and the Petty Projection Inequality, (sharp) isoperimetric inequalities are derived for the projection measures (Quermassintegrale) of a convex body. These projection measure inequalities, which involve mixed projection bodies (zonoids), are shown to be strengthened versions of the classical inequalities between the projection measures of a convex body. The inequality obtained for the volume of mixed bodies is also used to derive a form of the Brunn-Minkowski inequality involving mixed bodies. As an application, inequalities are given between the projection measures of convex bodies and the mixed projection integrals of the bodies.


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DOI: http://dx.doi.org/10.1090/S0002-9947-1986-0825717-3
PII: S 0002-9947(1986)0825717-3
Keywords: Convex body, mixed area measure, mixed body, mixed volume, projection body, projection measure (Quermassintegrale), zonoid
Article copyright: © Copyright 1986 American Mathematical Society