Abstract
We provide a geometric characterization of the minimal and maximal minimizer of the prescribed curvature functionalP(E) −κ|E| among subsets of a Jordan domainΩwith no necks of radiusκ−1, for values ofκgreater 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 domainΩwhich has no necks of radiusr, for allr. Finally, we show that for such sets and volumes the isoperimetric profile is convex.
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