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- W2079679648 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 <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=i> <mml:semantics> <mml:mi>i</mml:mi> <mml:annotation encoding=application/x-tex>i</mml:annotation> </mml:semantics> </mml:math> </inline-formula>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." @default.
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- W2079679648 date "1985-01-01" @default.
- W2079679648 modified "2023-10-16" @default.
- W2079679648 title "Mixed projection inequalities" @default.
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