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.
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