Dr Georgios Domazakis georgios.domazakis@durham.ac.uk
Postdoctoral Research Associate
Rigidity for the perimeter inequality under Schwarz symmetrization
Domazakis, Georgios
Authors
Abstract
In this paper, we give necessary and sufficient conditions for the rigidity of the perimeter inequality under Schwarz symmetrization. The term rigidity refers to the situation in which the equality cases are only obtained by translations of the symmetric set. In particular, we prove that the sufficient conditions for rigidity provided in M. Barchiesi, F. Cagnetti and N. Fusco [Stability of the Steiner symmetrization of convex sets. J. Eur. Math. Soc. 15 (2013), 1245-1278.] are also necessary.
Citation
Domazakis, G. (2024). Rigidity for the perimeter inequality under Schwarz symmetrization. Proceedings of the Royal Society of Edinburgh Section A: Mathematics, 1-27. https://doi.org/10.1017/prm.2024.59
| Journal Article Type | Article |
|---|---|
| Acceptance Date | May 3, 2024 |
| Online Publication Date | Jun 3, 2024 |
| Publication Date | Jun 3, 2024 |
| Deposit Date | Jun 27, 2024 |
| Publicly Available Date | Jun 27, 2024 |
| Journal | Proceedings of the Royal Society of Edinburgh: Section A Mathematics |
| Print ISSN | 0308-2105 |
| Electronic ISSN | 1473-7124 |
| Publisher | Cambridge University Press |
| Peer Reviewed | Peer Reviewed |
| Pages | 1-27 |
| DOI | https://doi.org/10.1017/prm.2024.59 |
| Public URL | https://durham-repository.worktribe.com/output/2504703 |
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Licence
http://creativecommons.org/licenses/by/4.0/
Publisher Licence URL
http://creativecommons.org/licenses/by/4.0/
Copyright Statement
This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (https://creativecommons.org/licenses/by/4.0/), which permits unrestricted re-use, distribution, and reproduction in any medium, provided the original work is properly cited.