On the singular points approached by the medial axis

Abstract

This paper develops the notion of superquadracity defined by L.Birbrair and M.Denkowski for subsets of R^n. In this regard, the main theorem of the paper establishes the relation between the superquadracity and non-empty intersection of the set and the closure of its medial axis. The further investigation concerns non C1 smooth points of the set.

The last version comes with a revised proof of Theorem 3.1 and an additional section about the C^1 singularities separated from the sets frontier and a more general setting