Metric properties of conflict sets

Lev Birbrair, Universidade Federal do Ceará

Let X and Y be two disjoint subsets of Rn. The conflict set of
X and Y is the set of points x, such that dist(x,X)=dist(x,Y).
Conflict sets can have singularities even in the case when X and Y
are smooth. We are going to discuss some general (not only generic)
properties of these singularities.