A General Isepiphanic Inequality
- 1 March 1984
- journal article
- Published by JSTOR in Proceedings of the American Mathematical Society
- Vol. 90 (3) , 415-421
- https://doi.org/10.2307/2044485
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.Keywords
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