Journal Home Page Cumulative Index List of all Volumes Complete Contentsof this Volume Previous Article Journal of Convex Analysis 28 (2021), No. 3, [final page numbers not yet available]Copyright Heldermann Verlag 2021 A Sufficient Criterion to Determine Planar Self-Cheeger Sets Giorgio Saracco Scuola Internazionale Superiore di Studi Avanzati, Trieste, Italy gsaracco@sissa.it [Abstract-pdf] We prove a sufficient criterion to determine if a planar set $\Omega$ minimizes the prescribed curvature functional $\mathcal{F}_\kappa[E]:=P(E)-\kappa|E|$ amongst $E\subset \Omega$. As a special case, we derive a sufficient criterion to determine if $\Omega$ is a self-Cheeger set, i.e.~if it minimizes the ratio $P(E)/|E|$ among all of its subsets. As a side effect we provide a way to build self-Cheeger sets. Keywords: Cheeger constant, inner Cheeger formula, self-Cheeger sets, perimeter minimizer, prescribed mean curvature. MSC: 49Q10; 35J93, 49Q20. [ Fulltext-pdf  (104  KB)] for subscribers only.