English

The double spherical cap rearrangement of planar sets

Functional Analysis 2025-10-02 v2

Abstract

This paper is devoted to the proof of an isoperimetric property of the double spherical cap rearrangement of planar sets under the assumption of disconnection of non-trivial spherical slices. Additionally, the higher-dimensional case is briefly discussed; in particular, an explicit counterexample is given, thus explaining why an analogous result cannot hold.

Keywords

Cite

@article{arxiv.2509.13889,
  title  = {The double spherical cap rearrangement of planar sets},
  author = {Chiara Gambicchia},
  journal= {arXiv preprint arXiv:2509.13889},
  year   = {2025}
}

Comments

19 pages, 5 figures