Cheeger sets for rotationally symmetric planar convex bodies

In this note we obtain some properties of the Cheeger set $C_\Omega$ asociated to a $k$-rotationally symmetric planar convex body $\Omega$. More precisely, we prove that $C_\Omega$ is also $k$-rotationally symmetric and touches all the edges of $\Omega$.
Comment: 9 pages, 5 figures