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This paper aims to establish a relation between the tangent cone of themedial axis of X at a given point a of R^n$ and the medial axis of the set ofpoints in X realising the distance d(a,X). As a consequence, a lower bound forthe dimension of the medial axis of X in terms of the dimension of the medialaxis of m(a) is obtained. This appears to be the missing link to the fulldescription of the medial axis' dimension. Further study of potentiallytroublesome points on the frontier of the medial axis is also provided,resulting in their characterisation in terms of the reaching radius.

The tangent cone, the dimension and the frontier of a medial axis