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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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Dual kinematic formulas
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by Gaoyong Zhang PDF
Trans. Amer. Math. Soc. 351 (1999), 985-995 Request permission

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.
References
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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
  • 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
  • © Copyright 1999 American Mathematical Society
  • 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