A note on Haussdorff geometry of polynomials (Q2762942)

The author introduces the notion of Hausdorff geometry of polynomials for investigation the location of the set of the critical points (zeros of the derivative) using the set of all zeros of a polynomial. On the one hand the introduction of the Hausdorff distance between the closed and bounded sets on the complex plane allows to represent in an elegant way the well known Gauss-Lucas' and Aziz' theorems as well Sendov's (mistakenly known as Ilieff's one), Schmeisser's and Phelps-Rodriquez conjectures. On the other hand a lot of new problems and conjectures are considered as for instance the location of critical points of a polynomial depends on the location of the zeros in the complex plane.