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1 results

  • A stability inequality for planar lens partition

  • Part of
  • Marco Bonacini, Riccardo Cristoferi, Ihsan Topaloglu
  • Journal:
    Proceedings of the Royal Society of Edinburgh. Section A: Mathematics , First View
    Published online by Cambridge University Press:
    27 January 2025, pp. 1-34
    • Article
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  • 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.