Gian Paolo Leonardi, Giorgio Saracco
Published 2021-08-24Version 1
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.
Comments: 27 pages, 5 figures
On the isoperimetric problem with double density
The $\varepsilon-\varepsilon^β$ property in the isoperimetric problem with double density, and the regularity of isoperimetric sets
Existence of isoperimetric sets with densities "converging from below" in $\mathbb{R}^N$
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