46 citations · 149 across the 14 of their papers we have counts for
20 papers
Mean Lipschitz-Killing curvatures for homogeneous random fractals
Jan Rataj, Steffen Winter, Martina Zähle
Homogeneous random fractals form a probabilistic extension of self-similar sets with more dependencies than in random recursive constructions. For such random fractals we consider…
Mean Euler characteristic of stationary random closed sets
Jan Rataj
The translative intersection formula of integral geometry yields an expression for the mean Euler characteristic of a stationary random closed set intersected with a fixed observat…
Smallness of the set of critical values of distance functions in two-dimensional Euclidean and Riemannian spaces
Jan Rataj, Ludek Zajicek
We study how small is the set of critical values of the distance function from a compact (resp. closed) set in the plane or in a connected complete two-dimensional Riemannian manif…
Dilation volumes of sets of finite perimeter
Markus Kiderlen, Jan Rataj
This paper analyzes the first order behavior (that is, the right sided derivative) of the volume of the dilation as converges to zero. Here and are subsets…
Flag representations of mixed volumes and mixed functionals of convex bodies
Daniel Hug, Jan Rataj, Wolfgang Weil
Mixed volumes of convex bodies in Euclidean space are of central importance in the Brunn-Minkowski theory. Representations for m…
On the structure of WDC sets
Dušan Pokorný, Jan Rataj, Luděk Zajíček
WDC sets in were recently defined as sublevel sets of DC functions (differences of convex functions) at weakly regular values. They form a natural and substantial g…