A short proof of principal kinematic formula and extensions

Rother, W.; Zähle, M.

doi:10.1090/S0002-9947-1990-0987167-X

A short proof of principal kinematic formula and extensions
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by W. Rother and M. Zähle

Trans. Amer. Math. Soc. 321 (1990), 547-558

DOI: https://doi.org/10.1090/S0002-9947-1990-0987167-X

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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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Normal cycles and second order rectifiable sets