Normal cycles and curvature measures of sets with d.c. boundary
Differential Geometry
2013-09-17 v4
Abstract
We show that for every compact domain in a Euclidean space with d.c. (delta-convex) boundary there exists a unique Legendrian cycle such that the associated curvature measures fulfil a local version of the Gauss-Bonnet formula. This was known in dimensions two and three and was open in higher dimensions. In fact, we show this property for a larger class of sets including also lower-dimensional sets. We also describe the local index function of the Legendrian cycles and we show that the associated curvature measures fulfill the Crofton formula.
Keywords
Cite
@article{arxiv.1209.2305,
title = {Normal cycles and curvature measures of sets with d.c. boundary},
author = {Dusan Pokorny and Jan Rataj},
journal= {arXiv preprint arXiv:1209.2305},
year = {2013}
}
Comments
22 pp, corrected version