Minimizers of the prescribed curvature functional in a Jordan domain with no necks

Leonardi, Gian Paolo; Saracco, Giorgio

ESAIM: Control, Optimisation and Calculus of Variations, Tome 26 (2020), article no. 76.

Suite au passage du modèle économique de la revue en S20, le texte intégral des articles des années 2019 et 2020 est accessible uniquement sur le site de l'éditeur et est réservé aux abonnés.

We provide a geometric characterization of the minimal and maximal minimizer of the prescribed curvature functional P(E) − κ|E| among subsets of a Jordan domain Ω with no necks of radius κ⁻¹, for values of κ greater than or equal to the Cheeger constant of Ω. As an application, we describe all minimizers of the isoperimetric profile for volumes greater than the volume of the minimal Cheeger set, relative to a Jordan domain Ω which has no necks of radius r, for all r. Finally, we show that for such sets and volumes the isoperimetric profile is convex.

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