On Boundaries of $\epsilon$-neighbourhoods of Planar Sets: Singularities, Global Structure, and Curvature

Jeroen S. W. Lamb, Martin Rasmussen, Kalle G. Timperi

We study the geometry, topological properties and smoothness of the boundaries of closed $\epsilon$-neighbourhoods $E_\varepsilon = \{x \in \mathbb{R}^2 \, : \, \textrm{dist}(x,…