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Abstract: It is shown that su#ciently close outer and inner parallel sets to a d- dimensional Lipschitz manifold in R with boundary have locally positive reach and the normal cycle of the Lipschitz manifold can be defined as limit of normal cycles of the parallel sets in the flat seminorms for currents, provided that the normal cycles of the parallel set have locally bounded mass. The Gauss-Bonnet formula and principal kinematic formula are proved for these normal cycles. It is shown that locally... (Update)
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BibTeX entry: (Update)
@misc{ rataj-normal,
author = "J. Rataj and M. Zähle",
title = "Normal cycles of Lipschitz manifolds by approximation with parallel sets",
url = "citeseer.ist.psu.edu/621417.html" }
Citations (may not include all citations):13 New York (context) - Clarke, Nonsmooth et al. - 1983
12 Springer Verlag (context) - Federer, Theory - 1969
1 erential Geometry (context) - Fu, measures et al. - 1989
1 Zahle: Remarks on mixed curvature measures for sets with pos.. (context) - Rataj - 2002
1 Kuppe: Integral geometry of tame sets (context) - Brocker - 2000
1 Zalgaller: Intrinsic geometry of surfaces (context) - Alexandrov - 1967
1 Schatzle: Intersections and translative integral formulas fo.. (context) - Hug - 2001
1 Zahle: Curvatures and currents for unions of sets with posit.. (context) - Rataj - 2001
1 Zahle: Mixed curvature measures for sets of positive reach a.. (context) - Rataj - 1995
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