A strong quantitative form of the fractional isoperimetric inequality
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866911275304353792 |
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| author | Cinti, Eleonora Merlino, Enzo Maria Ruffini, Berardo |
| author_facet | Cinti, Eleonora Merlino, Enzo Maria Ruffini, Berardo |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_14885 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A strong quantitative form of the fractional isoperimetric inequality Cinti, Eleonora Merlino, Enzo Maria Ruffini, Berardo Analysis of PDEs Differential Geometry Functional Analysis Metric Geometry Primary 49Q20, 49K40, Secondary 28A75, 49Q10 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. |
| title | A strong quantitative form of the fractional isoperimetric inequality |
| topic | Analysis of PDEs Differential Geometry Functional Analysis Metric Geometry Primary 49Q20, 49K40, Secondary 28A75, 49Q10 |
| url | https://arxiv.org/abs/2511.14885 |