Cheeger sets for rotationally symmetric planar convex bodies

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