On the isoperimetric deficit in Gauss space

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Robust Optimality of Gaussian Noise Stability (2012, background): “[13], who showed that the answer was “yes,” and gave a bound that depended on both δ and n.”
Sharp isoperimetric inequalities via the ABP method (2013, unknown): “For example, in R n with the Gaussian weight w(x) = e −| x | 2 all the minimizers are half-spaces [3, 16], and with w(x) = e | x | 2 all the minimizers are balls centered at the origin [46].”
A two-sided estimate for the Gaussian noise stability deficit (2013, methodology): “The first robustness estimate for the Gaussian isoperimetric inequality was proven by Cianchi-Fusco-Maggi-Pratelli in [7], and is based on a geometric approach.”
Robust dimension free isoperimetry in Gaussian space (2012, methodology): “The authors would like to thank the following colleagues: Franck Barthe and Almut Buchard for interesting discussions at the beginning of the project and for comments on the draft of the manuscript, Michel Ledoux for pointing out several places where our arguments in the previous Arxived version cou”
A Selection Principle for the Sharp Quantitative Isoperimetric Inequality (2010, background): “Since the publication of [19] the study of quantitative forms of various geometric and functional inequalities has received a new impulse (see for instance [8,13,14,18,20] and the review paper [26]).”