Bobkov, S. A functional form of the isoperimetric inequality for the Gaussian measure. (English) Zbl 0838.60013 J. Funct. Anal. 135, No. 1, 39-49 (1996). Summary: Let \(g\) be a smooth function on \(\mathbb{R}^n\) with values in \([0,1]\). Using the isoperimetric property of the Gaussian measure, it is proved that \[ \varphi \bigl (\Phi^{-1} ({\mathbf E} g) \bigr) - {\mathbf E} \varphi \bigl( \Phi^{-1} (g) \bigr) \leq {\mathbf E} |\nabla g |. \] Conversely, this inequality implies the isoperimetric property of the Gaussian measure. Cited in 2 ReviewsCited in 13 Documents MSC: 60E15 Inequalities; stochastic orderings 60G15 Gaussian processes Keywords:isoperimetric property of the Gaussian measure PDFBibTeX XMLCite \textit{S. Bobkov}, J. Funct. Anal. 135, No. 1, 39--49 (1996; Zbl 0838.60013) Full Text: DOI Link