### Abstract

A sharp affine isoperimetric inequality is established which gives a sharp lower bound for the volume of the polar body. It is shown that equality occurs in the inequality if and only if the body is a simplex.

Original language | English (US) |
---|---|

Pages (from-to) | 163-178 |

Number of pages | 16 |

Journal | Journal of Differential Geometry |

Volume | 84 |

Issue number | 1 |

State | Published - Jan 2010 |

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### ASJC Scopus subject areas

- Algebra and Number Theory
- Analysis
- Geometry and Topology

### Cite this

*Journal of Differential Geometry*,

*84*(1), 163-178.

**A volume inequality for polar bodies.** / Lutwak, Erwin; Yang, Deane; Zhang, Gaoyong.

Research output: Contribution to journal › Article

*Journal of Differential Geometry*, vol. 84, no. 1, pp. 163-178.

}

TY - JOUR

T1 - A volume inequality for polar bodies

AU - Lutwak, Erwin

AU - Yang, Deane

AU - Zhang, Gaoyong

PY - 2010/1

Y1 - 2010/1

N2 - A sharp affine isoperimetric inequality is established which gives a sharp lower bound for the volume of the polar body. It is shown that equality occurs in the inequality if and only if the body is a simplex.

AB - A sharp affine isoperimetric inequality is established which gives a sharp lower bound for the volume of the polar body. It is shown that equality occurs in the inequality if and only if the body is a simplex.

UR - http://www.scopus.com/inward/record.url?scp=77951183272&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=77951183272&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:77951183272

VL - 84

SP - 163

EP - 178

JO - Journal of Differential Geometry

JF - Journal of Differential Geometry

SN - 0022-040X

IS - 1

ER -