A quantitative dimension free isoperimetric inequality for the fractional Gaussian perimeter

We prove a quantitative isoperimetric inequality for the Gaussian fractional perimeter using extension techniques. Though the exponent of the Fraenkel asymmetry is not sharp, the constant appearing in the inequality does not depend on the dimension but only on the Gaussian volume of the set and on t...

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Bibliographic Details
Published inarXiv.org
Main Authors Carbotti, Alessandro, Cito, Simone, La Manna, Domenico Angelo, Pallara, Diego
Format Paper
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 21.02.2022
Subjects
Inequality
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Summary:We prove a quantitative isoperimetric inequality for the Gaussian fractional perimeter using extension techniques. Though the exponent of the Fraenkel asymmetry is not sharp, the constant appearing in the inequality does not depend on the dimension but only on the Gaussian volume of the set and on the fractional parameter.
ISSN:2331-8422