A strong quantitative form of the fractional isoperimetric inequality
Analysis of PDEs
2025-11-20 v1 Differential Geometry
Functional Analysis
Metric Geometry
Abstract
We show a strong version of the fractional quantitative isoperimetric inequality, in which the isoperimetric deficit controls not only the Fraenkel asymmetry but also a sort of oscillation of the boundary. This generalizes the local result by Fusco and Julin in \cite{FJ}. The proof follows a regularization process as in \cite{FJ} but it is quite different in its spirit. Then, as a consequence of the quantitative inequality, we prove some stability estimates for a fractional Cheeger inequality.
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Cite
@article{arxiv.2511.14885,
title = {A strong quantitative form of the fractional isoperimetric inequality},
author = {Eleonora Cinti and Enzo Maria Merlino and Berardo Ruffini},
journal= {arXiv preprint arXiv:2511.14885},
year = {2025}
}
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35 pages