Maciej P. Denkowski

Medial Axis and Singularities

This paper is devoted to the study of the medial axes of sets definable in polynomially bounded o-minimal structures, i.e. the sets of points with more than one closest point with respect to the Euclidean distance. Our point of view is that of singularity theory. While trying to make the paper self-contained, we gather here also a large bunch of basic results. Our main interest, however, goes to the characterization of those singular points of a definable, closed set

Multiplicity and the pull-back problem

Xsubset {mathbb {R}}^n

A note on the Nullstellensatz for c-holomorphic functions

X⊂Rn, which are reached by the medial axis.

The Łojasiewicz exponent of c-holomorphic mappings

We prove that given a holomorphic family of holomorphic functions with isolated singularities at the origin and constant Milnor number, it is possible to obtain the gradient inequality with a uniform exponent.

On the Kuratowski convergence of analytic sets

We discuss a formula of S. Spodzieja and generalize it for the isolated improper Achilles-Tworzewski-Winiarski intersection index. As an application we give a simple proof of a result of P. Ebenfelt and L. Rothschild: if

Residue calculus for c-holomorphic functions

{Fcolon (mathbb{C}^m,0)to (mathbb{C}^m,0)}