English

The isoperimetric problem in $2$d domains without necks

Analysis of PDEs 2022-02-08 v2

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.

Keywords

Cite

@article{arxiv.2108.10762,
  title  = {The isoperimetric problem in $2$d domains without necks},
  author = {Gian Paolo Leonardi and Giorgio Saracco},
  journal= {arXiv preprint arXiv:2108.10762},
  year   = {2022}
}

Comments

29 pages, 7 figures

R2 v1 2026-06-24T05:22:55.786Z