Barthe, F.; Maurey, B. Some remarks on isoperimetry of Gaussian type. (English) Zbl 0964.60018 Ann. Inst. Henri Poincaré, Probab. Stat. 36, No. 4, 419-434 (2000). The authors give a martingale proof of the Gaussian isoperimetry. This also yields S. G. Bobkov’s inequality [Ann. Probab. 25, No. 1, 206-214 (1997; Zbl 0883.60031)] for the two-point space and its extension to non-symmetric Bernoulli measures. The equivalence of different forms of Gaussian type isoperimetry is shown, which allows the authors to prove a sharp form of Bobkov’s inequality for the sphere and to get isoperimetric estimates for the unit cube. Reviewer: Marius Iosifescu (Bucureşti) Cited in 1 ReviewCited in 30 Documents MSC: 60E15 Inequalities; stochastic orderings 60G15 Gaussian processes 49Q20 Variational problems in a geometric measure-theoretic setting Keywords:isoperimetry; Gaussian measure Citations:Zbl 0883.60031 PDFBibTeX XMLCite \textit{F. Barthe} and \textit{B. Maurey}, Ann. Inst. Henri Poincaré, Probab. Stat. 36, No. 4, 419--434 (2000; Zbl 0964.60018) Full Text: DOI Numdam EuDML