On hypersurfaces of positive reach, alternating Steiner formulae and Hadwiger's Problem
Differential Geometry
2013-04-16 v1
Abstract
We give new characterisations of sets of positive reach and show that a closed hypersurface has positive reach if and only if it is of class . These results are then used to prove new alternating Steiner formul{\ae} for hypersurfaces of positive reach. Furthermore, it will turn out that every hypersurface that satisfies an alternating Steiner formula has positive reach. Finally, we provide a new solution to a problem by Hadwiger on convex sets and prove long time existence for the gradient flow of mean breadth.
Keywords
Cite
@article{arxiv.1304.4179,
title = {On hypersurfaces of positive reach, alternating Steiner formulae and Hadwiger's Problem},
author = {Sebastian Scholtes},
journal= {arXiv preprint arXiv:1304.4179},
year = {2013}
}