论文信息 - A functional form of the isoperimetric inequality for the Gaussian measure

A functional form of the isoperimetric inequality for the Gaussian measure

Abstract Letgbe a smooth function on R nwith values in [0, 1]. Using the isoperimetric property of the Gaussian measure, itis proved thatφ(Φ−1(Eg))−Eφ(Φ−1(g))⩽E|∇g|. Conversely, this inequality implies the isoperimetric property of the Gaussian measure.

Sergey G. Bobkov | S. Bobkov

[1] L. Gross. LOGARITHMIC SOBOLEV INEQUALITIES. , 1975 .

[2] C. Borell. The Brunn-Minkowski inequality in Gauss space , 1975 .

[3] O. Rothaus. Analytic inequalities, isoperimetric inequalities and logarithmic Sobolev inequalities , 1985 .

[4] Isopérimétrie et inégalités de Sobolev logarithmiques gaussiennes , 1988 .

[5] V. Sudakov,et al. Extremal properties of half-spaces for spherically invariant measures , 1978 .

[6] H. Fédérer. Geometric Measure Theory , 1969 .

[7] M. Ledoux,et al. Isoperimetry and Gaussian analysis , 1996 .

[8] L. Gross. Logarithmic Sobolev inequalities and contractivity properties of semigroups , 1993 .

[9] A. Ehrhard. Inégalités isopérimétriques et intégrales de Dirichlet gaussiennes , 1984 .

[10] R. Osserman. The isoperimetric inequality , 1978 .

[11] M. Ledoux. Semigroup proofs of the isoperimetric inequality in Euclidean and Gauss space , 1994 .

[12] A proof of a logarithmic Sobolev inequality , 1993 .

[13] Barry Simon,et al. Ultracontractivity and the Heat Kernel for Schrijdinger Operators and Dirichlet Laplacians , 1987 .

[14] G. Pisier. Probabilistic methods in the geometry of Banach spaces , 1986 .

[15] M. Talagrand. Isoperimetry, logarithmic sobolev inequalities on the discrete cube, and margulis' graph connectivity theorem , 1993 .