Abstract
It is shown that sufficiently close inner parallel sets and closures of the complements of outer parallel sets to a d-dimensional Lipschitz manifold in R d 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 finite unions of non-osculating sets with positive reach of full dimension, as well as the closures of their complements, admit such a definition of normal cycle.
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