Dual kinematic formulas

Author:
Gaoyong Zhang

Journal:
Trans. Amer. Math. Soc. **351** (1999), 985-995

MSC (1991):
Primary 52A22; Secondary 53C65, 60D05

DOI:
https://doi.org/10.1090/S0002-9947-99-02053-X

MathSciNet review:
1443203

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Abstract | References | Similar Articles | Additional Information

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.

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Additional Information

**Gaoyong Zhang**

Affiliation:
School of Mathematics, Institute for Advanced Study and Department of Mathematics, University of Pennsylvania, Philadelphia, Pennsylvania 19104

Address at time of publication:
Department of Mathematics, Polytechnic University, 6 Metrotech Center, Brooklyn, New York 11201

Email:
gzhang@math.poly.edu

DOI:
https://doi.org/10.1090/S0002-9947-99-02053-X

Keywords:
Kinematic formula,
dual quermassintegral,
chord power integral,
dual mixed volume,
star body,
convex body,
geometric probability

Received by editor(s):
September 13, 1996

Received by editor(s) in revised form:
December 2, 1996

Additional Notes:
Research supported partially by NSF Grant DMS–9504913.

Dedicated:
Dedicated to Professor De-lin Ren on the occasion of his 65th birthday

Article copyright:
© Copyright 1999
American Mathematical Society