### 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 | |

State | Published - 1984 |

### Fingerprint

### Keywords

- Convex body
- Projection body
- Projection measure (Quermassintegrale)

### ASJC Scopus subject areas

- Mathematics(all)
- Applied Mathematics

### Cite this

**A general isepiphanic inequality.** / Lutwak, Erwin.

Research output: Contribution to journal › Article

*Proceedings of the American Mathematical Society*, vol. 90, no. 3, pp. 415-421. https://doi.org/10.1090/S0002-9939-1984-0728360-3

}

TY - JOUR

T1 - A general isepiphanic inequality

AU - Lutwak, Erwin

PY - 1984

Y1 - 1984

N2 - 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.

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)

UR - http://www.scopus.com/inward/record.url?scp=0005877234&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0005877234&partnerID=8YFLogxK

U2 - 10.1090/S0002-9939-1984-0728360-3

DO - 10.1090/S0002-9939-1984-0728360-3

M3 - Article

VL - 90

SP - 415

EP - 421

JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

SN - 0002-9939

IS - 3

ER -