### Abstract

We establish kinematic formulas for dual quermassintegrals of star bodies and for chord power integrals of convex bodies by using dual mixed volumes. These formulas are extensions of the fundamental kinematic formula involving quermassintegrals to the cases of dual quermassintegrals and chord power integrals. Applications to geometric probability are considered.

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

Pages (from-to) | 985-995 |

Number of pages | 11 |

Journal | Transactions of the American Mathematical Society |

Volume | 351 |

Issue number | 3 |

State | Published - 1999 |

### Fingerprint

### Keywords

- Chord power integral
- Convex body
- Dual mixed volume
- Dual quermassintegral
- Geometric probability
- Kinematic formula
- Star body

### ASJC Scopus subject areas

- Mathematics(all)

### Cite this

*Transactions of the American Mathematical Society*,

*351*(3), 985-995.

**Dual kinematic formulas.** / Zhang, Gaoyong.

Research output: Contribution to journal › Article

*Transactions of the American Mathematical Society*, vol. 351, no. 3, pp. 985-995.

}

TY - JOUR

T1 - Dual kinematic formulas

AU - Zhang, Gaoyong

PY - 1999

Y1 - 1999

N2 - We establish kinematic formulas for dual quermassintegrals of star bodies and for chord power integrals of convex bodies by using dual mixed volumes. These formulas are extensions of the fundamental kinematic formula involving quermassintegrals to the cases of dual quermassintegrals and chord power integrals. Applications to geometric probability are considered.

AB - We establish kinematic formulas for dual quermassintegrals of star bodies and for chord power integrals of convex bodies by using dual mixed volumes. These formulas are extensions of the fundamental kinematic formula involving quermassintegrals to the cases of dual quermassintegrals and chord power integrals. Applications to geometric probability are considered.

KW - Chord power integral

KW - Convex body

KW - Dual mixed volume

KW - Dual quermassintegral

KW - Geometric probability

KW - Kinematic formula

KW - Star body

UR - http://www.scopus.com/inward/record.url?scp=0346016730&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0346016730&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0346016730

VL - 351

SP - 985

EP - 995

JO - Transactions of the American Mathematical Society

JF - Transactions of the American Mathematical Society

SN - 0002-9947

IS - 3

ER -