Volume of Mixed Bodies
- 1 April 1986
- journal article
- Published by JSTOR in Transactions of the American Mathematical Society
- Vol. 294 (2) , 487-500
- https://doi.org/10.2307/2000195
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.Keywords
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