# On the Cheeger problem for rotationally invariant domains

@article{Bobkov2020OnTC, title={On the Cheeger problem for rotationally invariant domains}, author={Vladimir Bobkov and Enea Parini}, journal={manuscripta mathematica}, year={2020} }

We investigate the properties of the Cheeger sets of rotationally invariant, bounded domains $\Omega \subset \mathbb{R}^n$. For a rotationally invariant Cheeger set $C$, the free boundary $\partial C \cap \Omega$ consists of pieces of Delaunay surfaces, which are rotationally invariant surfaces of constant mean curvature. We show that if $\Omega$ is convex, then the free boundary of $C$ consists only of pieces of spheres and nodoids. This result remains valid for nonconvex domains when theβ¦Β

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