A general isepiphanic inequality

Lutwak, Erwin

doi:10.1090/S0002-9939-1984-0728360-3

A general isepiphanic inequality
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Proc. Amer. Math. Soc. 90 (1984), 415-421 Request permission

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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