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arXiv · 2108.10762

The isoperimetric problem in $2$d domains without necks

Gian Paolo Leonardi·Giorgio Saracco
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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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Gian Paolo Leonardi, Giorgio Saracco. 2021-08-24. The isoperimetric problem in $2$d domains without necks. https://doi.org/10.1007/s00526-021-02153-9

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