D. Pokorný

activity

20132020

collaborators

4 papers

math.CA2020

A characterization of sets in $R^{2}$ with DC distance function

Dušan Pokorný, Luděk Zajíček

We give a complete characterization of closed sets $F \subset R^{2}$ whose distance function $d_{F} := dist (\cdot, F)$ is DC (i.e., is the difference of two convex func…

math.MG2019

Curvatures for unions of WDC sets

Dušan Pokorný

We prove the existence of the curvature measures for a class of $U_{WDC}$ sets, which is a direct generalization of $U_{PR}$ sets studied by Rataj and Zähle. More…

math.CA2019

On sets in $R^{d}$ with DC distance function

Dušan Pokorný, Luděk Zajíček

We study closed sets $F \subset R^{d}$ whose distance function $d_{F} := dist (\cdot, F)$ is DC (i.e., is the difference of two convex functions on $R^{d}$ ). Our…

math.FA2013

Nonconvex Lipschitz function in plane which is locally convex outside a discontinuum

Dusan Pokorny

We construct a Lipschitz function on $\er^{2}$ which is locally convex on the complement of some totally disconnected compact set but not convex. Existence of such function disprov…

A characterization of sets in R2 with DC distance function

Curvatures for unions of WDC sets

On sets in Rd with DC distance function

Nonconvex Lipschitz function in plane which is locally convex outside a discontinuum

A characterization of sets in $R^{2}$ with DC distance function

On sets in $R^{d}$ with DC distance function