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math.MG2026
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…
math.MG2019
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…
math.MG2017
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…