Unbounded components of the singular set of the distance function in $\mathbb R^n$

Abstract

Given a closed set F ⊆ ℝn, the set ∑F of all points at which the metric projection onto F is multi-valued is nonempty if and only if F is nonconvex. The authors analyze such a set, characterizing the unbounded connected components of ∑F. For F compact, the existence of an asymptote for any unbounded component of ∑F is obtained. ©2001 American Mathematical Society.