4 papers
A characterization of the local structure of two-dimensional sets with positive reach
Jan Rataj, Ludek Zajicek
The main result of the article is a complete characterization of the local structure of two-dimensional sets with positive reach in . We also present a more elementary proof o…
On the (outer) Minkowski content with lower-dimensional structuring element
Markus Kiderlen, Jan Rataj
Given a convex body (structuring element) and a set in a Euclidean space, we consider the -Minkowski content of . It is defined as the usual isotropic Minkowski conte…
Mean Minkowski content and mean fractal curvatures of random self-similar code tree fractals
Jan Rataj, Steffen Winter, Martina Zähle
We consider a class of random self-similar fractals based on code trees which includes random recursive, homogeneous and V-variable fractals and many more. For such random fractals…
On volume and surface area of parallel sets. II. Surface measures and (non-)differentiability of the volume
Jan Rataj, Steffen Winter
We prove that at differentiability points of the volume function of a compact set (associating to the volume of the -parallel set of ), t…