Inserted: 24 aug 2021
Last Updated: 30 aug 2021
We give a complete characterization of all isoperimetric sets contained in a domain of the Euclidean plane, that is bounded by a Jordan curve and satisfies a no-neck property. Further, we prove that the isoperimetric profile of such domain is convex above the volume of the largest ball contained in it, and that its square is globally convex.
Keywords: convexity, prescribed mean curvature, perimeter minimizer, isoperimetric profile