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arXiv · 2509.13889

The double spherical cap rearrangement of planar sets

Chiara Gambicchia
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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.

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Chiara Gambicchia. 2025-09-17. The double spherical cap rearrangement of planar sets. https://arxiv.org/abs/2509.13889

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