46 citations · 149 across the 14 of their papers we have counts for
10 papers · 1 filter
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…
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…
Mixed curvature measures of translative integral geometry
Daniel Hug, Jan Rataj
The curvature measures of a set with singularities are measures concentrated on the normal bundle of , which describe the local geometry of the set . For given finitely m…
On the structure of sets with positive reach
Jan Rataj, Ludek Zajicek
We give a complete characterization of compact sets with positive reach (=proximally sets) in the plane and of one-dimensional sets with positive reach in . Fu…
A flag representation of projection functions
Paul Goodey, Wolfram Hinderer, Daniel Hug +2
The th projection function of a convex body is a function on the Grassmannian which measures the -dimensional volume…