A general isepiphanic inequality

Erwin Lutwak

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

A general isepiphanic inequality

Erwin Lutwak

Mathematics

Research output: Contribution to journal › Article › peer-review

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 brightnees 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.

Original language	English (US)
Pages (from-to)	415-421
Number of pages	7
Journal	Proceedings of the American Mathematical Society
Volume	90
Issue number	3
DOIs	https://doi.org/10.1090/S0002-9939-1984-0728360-3
State	Published - Mar 1984

Keywords

Convex body
Projection body
Projection measure (Quermassintegrale)

ASJC Scopus subject areas

Mathematics(all)
Applied Mathematics

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10.1090/S0002-9939-1984-0728360-3

Cite this

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AB - 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 brightnees 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.

KW - Convex body

KW - Projection body

KW - Projection measure (Quermassintegrale)

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JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

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ER -

A general isepiphanic inequality

Abstract

Keywords

ASJC Scopus subject areas

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