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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Dual kinematic formulas


Author: Gaoyong Zhang
Journal: Trans. Amer. Math. Soc. 351 (1999), 985-995
MSC (1991): Primary 52A22; Secondary 53C65, 60D05
MathSciNet review: 1443203
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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: http://dx.doi.org/10.1090/S0002-9947-99-02053-X
PII: S 0002-9947(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