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Transactions of the American Mathematical Society

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

 

 

A short proof of principal kinematic formula and extensions


Authors: W. Rother and M. Zähle
Journal: Trans. Amer. Math. Soc. 321 (1990), 547-558
MSC: Primary 53C65; Secondary 49Q15, 58A25
MathSciNet review: 987167
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Abstract: Federer's extension of the classical principal kinematic formula of integral geometry to sets with positive reach is proved in a direct way by means of generalised unit normal bundles, associated currents, and the coarea theorem. This enables us to extend the relation to more general sets. At the same time we get a short proof for the well-known variants from convex geometry and differential geometry.


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DOI: https://doi.org/10.1090/S0002-9947-1990-0987167-X
Article copyright: © Copyright 1990 American Mathematical Society