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.
The isoperimetric problem in 2d domains without necks / Leonardi G.P.; Saracco G.. - In: CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS. - ISSN 0944-2669. - ELETTRONICO. - 61:(2022), pp. 56.1-56.23. [10.1007/s00526-021-02153-9]
The isoperimetric problem in 2d domains without necks
Saracco G.
2022
Abstract
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.
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