Sharp dimension free quantitative estimates for the Gaussian isoperimetric inequality

Abstract

We provide a full quantitative version of the Gaussian isoperimetric inequality. Our estimate is independent of the dimension, sharp on the decay rate with respect to the asymmetry and with optimal dependence on the mass.

References in corpus (2)

• Faber-Krahn inequalities in sharp quantitative form
• A two-sided estimate for the Gaussian noise stability deficit

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• Quantitative isoperimetric inequalities for classical capillarity problems
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• A remark on a conjecture on the symmetric Gaussian Problem