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arXiv · 2511.14885

A strong quantitative form of the fractional isoperimetric inequality

Eleonora Cinti·Enzo Maria Merlino·Berardo Ruffini
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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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Eleonora Cinti, Enzo Maria Merlino, Berardo Ruffini. 2025-11-18. A strong quantitative form of the fractional isoperimetric inequality. https://arxiv.org/abs/2511.14885

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