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Some remarks on isoperimetry of Gaussian type. (English) Zbl 0964.60018

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.

MSC:

60E15 Inequalities; stochastic orderings
60G15 Gaussian processes
49Q20 Variational problems in a geometric measure-theoretic setting

Citations:

Zbl 0883.60031
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