Abstract

We prove a sufficient criterion to determine if a planar set Ω\Omega minimizes the prescribed curvature functional Fκ[E]:=P(E)−κ∣E∣\mathcal{F}_\kappa[E]:=P(E)-\kappa|E| amongst E⊂ΩE\subset \Omega. As a special case, we derive a sufficient criterion to determine if Ω\Omega is a self-Cheeger set, i.e. if it minimizes the ratio P(E)/∣E∣P(E)/|E| among all of its subsets. As a side effect we provide a way to build self-Cheeger sets.

Author information

Contact details are reproduced from the original publication and may be historical.

Giorgio Saracco

Scuola Internazionale Superiore di Studi Avanzati, Trieste, Italy

gsaracco@sissa.it

Keywords

  • Cheeger constant
  • inner Cheeger formula
  • self-Cheeger sets
  • perimeter minimizer
  • prescribed mean curvature

Mathematics Subject Classification

49Q10; 35J93, 49Q20

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Suggested citation

G. Saracco. “A Sufficient Criterion to Determine Planar Self-Cheeger Sets.” Journal of Convex Analysis 28 (2021), No. 3, 951–958. https://doi.org/10.68381/jca28055

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Published by Heldermann Verlag, 2021. Rights now held by Banach Press.