A quantitative isoperimetric inequality for fractional perimeters
Nicola Fusco, Vincent Millot, Massimiliano Morini
TL;DR
This paper improves a recent isoperimetric inequality for fractional perimeters by providing a quantitative version, enhancing understanding of nonlocal geometric inequalities.
Contribution
The paper introduces a quantitative refinement of Frank and Seiringer's isoperimetric inequality for fractional perimeters, advancing the analysis of nonlocal geometric functionals.
Findings
Established a quantitative form of the fractional perimeter isoperimetric inequality
Enhanced the understanding of nonlocal geometric inequalities
Provided sharper bounds for fractional perimeter minimizers
Abstract
Recently Frank and Seiringer have shown an isoperimetric inequality for nonlocal perimeter functionals arising from Sobolev seminorms of fractional order. This isoperimetric inequality is improved here in a quantitative form.
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