@article{Pikuta_2003, title={On sets of constant distance from a planar set}, volume={21}, url={https://apcz.umk.pl/TMNA/article/view/TMNA.2003.022}, abstractNote={In this paper we prove that $d$-boundaries
$$
D_d=\{x:\roman{dist}( x,Z) =d\} $$ of a
compact $Z \subset \mathbb{R}^{2}$ are closed absolutely continuous
curves for $d$ greater than some constant depending on $Z$. It is
also shown that $D_d$ is a trajectory of solution to the Cauchy
Problem of a differential equation with a discontinuous right-hand
side.}, number={2}, journal={Topological Methods in Nonlinear Analysis}, author={Pikuta, Piotr}, year={2003}, month={Jun.}, pages={369–374} }