Calculus of Variations and Geometric Measure Theory
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G. P. Leonardi - G. Saracco

The isoperimetric problem in $2$d domains without necks

created by saracco on 24 Aug 2021
modified on 30 Aug 2021


Submitted Paper

Inserted: 24 aug 2021
Last Updated: 30 aug 2021

Year: 2021

ArXiv: 2108.10762 PDF


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


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