A stability inequality for planar lens partition
Abstract Recently it has been shown that the unique local perimeter minimizing partitioning of the plane into three regions, where one region has finite area and the other two have infinite measure, is given by the so-called standard lens partition. Here we prove a sharp stability inequality for the standard lens, hence strengthening the local minimality of the lens partition in a quantitative form. As an application of this stability result we consider a nonlocal perturbation of an isoperimetric problem.
Authors
- Riccardo Cristoferi (ORCID: https://orcid.org/0000-0001-7086-1269)
- Marco Bonacini (ORCID: https://orcid.org/0000-0003-1837-6578)
- Ihsan Topaloğlu (ORCID: https://orcid.org/0000-0003-4584-156X)
Institutions
- Radboud University Nijmegen (NL)
- Virginia Commonwealth University (US)
- University of Trento (IT)
Publication Details
- Journal
- Proceedings of the Royal Society of Edinburgh Section A Mathematics
- Published
- 2025-01-27
- DOI
- https://doi.org/10.1017/prm.2025.2
- Primary Topic
- Point processes and geometric inequalities
- Type
- article
- Field-Weighted Citation Impact
- 0.00
Funders
- National Science Foundation
- Alexander von Humboldt-Stiftung
- Istituto Nazionale di Alta Matematica "Francesco Severi"
- European Commission
- Nederlandse Organisatie voor Wetenschappelijk Onderzoek