Simple closed curves contained in~$\epsilon$-boundaries of planar sets

Aleksei Volkov, Mikhail Patrakeev

The $\epsilon$-boundary of a set $A\subseteq {\mathbb{R}}^2$ is the set $\{p\in {\mathbb{R}}^2:\ddot{I}(p,A)=\epsilon \}$, where $\ddot{I}$ is the Euclidean distance. We prove that if $…