Geodesic
A Sufficient Criterion to Determine Planar Self-Cheeger Sets
Journal of convex analysis, Tome 28 (2021) no. 3, pp. 951-958
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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.
Classification : 49Q10, 35J93, 49Q20
Mots-clés : Cheeger constant, inner Cheeger formula, self-Cheeger sets, perimeter minimizer, prescribed mean curvature 
@article{JCA_2021_28_3_JCA_2021_28_3_a14,
     author = {G. Saracco},
     title = {A {Sufficient} {Criterion} to {Determine} {Planar} {Self-Cheeger} {Sets}},
     journal = {Journal of convex analysis},
     pages = {951--958},
     year = {2021},
     volume = {28},
     number = {3},
     url = {http://geodesic.mathdoc.fr/item/JCA_2021_28_3_JCA_2021_28_3_a14/}
}
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G. Saracco. A Sufficient Criterion to Determine Planar Self-Cheeger Sets. Journal of convex analysis, Tome 28 (2021) no. 3, pp. 951-958. http://geodesic.mathdoc.fr/item/JCA_2021_28_3_JCA_2021_28_3_a14/