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Mixed projection inequalities


Author: Erwin Lutwak
Journal: Trans. Amer. Math. Soc. 287 (1985), 91-105
MSC: Primary 52A40
DOI: https://doi.org/10.1090/S0002-9947-1985-0766208-7
MathSciNet review: 766208
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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.


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Additional Information

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

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