Calculus of Variations and Geometric Measure Theory

G. P. Leonardi - G. Saracco

The isoperimetric problem in $2$d domains without necks

created by saracco on 24 Aug 2021
modified on 05 Feb 2022


Published Paper

Inserted: 24 aug 2021
Last Updated: 5 feb 2022

Journal: Calc. Var. Partial Differential Equations
Volume: 61
Number: 2
Pages: 56
Year: 2022
Doi: 10.1007/s00526-021-02153-9

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