A functional form of the isoperimetric inequality for the Gaussian measure

Journal of Functional Analysis

Volumn 135, Issue 1, 1996, Pages 39-49

  Bobkov, S ^a,b  

^a SYKTYVKAR STATE UNIVERSITY   (Russian Federation)

^b UNIVERSITY OF NORTH CAROLINA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0030577616     PISSN: 00221236     EISSN: None     Source Type: Journal    
DOI: 10.1006/jfan.1996.0002     Document Type: Article

References (18)

1. 1. S. AIDA, T. MASUDA, AND I. SHIGEKAWA, Logarithmic Sobolev inequalities and exponential integrability, preprint (1993).
2. 2. S. G. BOBKOV AND CH. HOUDRÉ, On some connections between Sobolev-type inequalities and isoperimetry, preprint (1994).
3. 3. C. BORELL, The Brunn-Minkowski inequality in Gauss space, Invent. Math. 30, Fasc. 2 (1975), 207-216.
4. 4. J.-D. DAVIES AND B. SIMON, Ultracontractivity and the heat kernel for Schrödinger operators and Dirichlet Laplacians, J. Funct. Anal. 59 (1984), 335-395.
5. 5. A. EHRHARD, Inégalités isopérimétriques et intégrales de Dirichlet gaussiennes, Ann. Sci. Ecole Norm. Sup. 17 (1984), 317-332.
6. 6. H. FEDERER, "Geometric Measure Theory," Springer-Verlag, Berlin, 1969.
7. 7. L. GROSS, Logarithmic Sobolev inequalities, Amer. J. Math. 97 (1975), 1061-1083.
8. 8. L. GROSS, Logarithmic Sobolev inequalities and contractivity properties of semigroups, in "Varenna, 1992," Lecture Notes in Mathematics, Vol. 1563, pp. 54-88, 1993.
9. 9. M. LEDOUX, Isopérimétrie et inégalités de Sobolev logarithmiques gaussiennes, C.R. Acad. Sci. Paris 306 (1988), 79-82.
10. 10. M. LEDOUX, Semigroup proofs of the isoperimetric inequality in Euclidean and Gauss space, Bull. Sci. Math, to appear.
11. 11. M. LEDOUX, Isoperimetry and Gaussian analysis, in "Ecole d'Eté de Probabilités de Saint-Flour," Lecture Notes in Mathematics Ser., Springer-Verlag, Berlin, 1994.
12. 12. R. OSSERMAN, The isoperimetric inequality, Bull. Amer. Math. Soc. 84 (1978), 1182-1238.
13. 13. E. PELLICCIA AND G. TALENTI, A proof of a logarithmic Sobolev inequality, Calc. Var. 1 (1993), 237-242.
14. 14. G. PISIER, Probabilistic methods in the geometry of Banach spaces, in "Probability and Analysis, Varenna 1985," pp. 167-214, Lecture Notes in Mathematics, Vol. 1206, Springer-Verlag, Berlin, 1986.
15. 15. O. S. ROTHAUS, Analytic inequalities, isoperimetric inequalities and logarithmic Sobolev inequalities, J. Funct. Anal. 64 (1985), 296-313.
16. 16. V. N. SUDAKOV AND B. S. TSIREL'SON, Extremal properties of half-spaces for spherically invariant measures, J. Soviet Math. 9 (1978), 9-18 [Engl. transl.]; Zap. Nauchn. Sem. Leningrad. Otdel. Mat. inst. Steklov. (LOMI) 41 (1974), 14-24.
17. 16. V. N. SUDAKOV AND B. S. TSIREL'SON, Extremal properties of half-spaces for spherically invariant measures, J. Soviet Math. 9 (1978), 9-18 [Engl. transl.]; Zap. Nauchn. Sem. Leningrad. Otdel. Mat. inst. Steklov. (LOMI) 41 (1974), 14-24.
18. 17. M. TALAGRAND, Isoperimetry, logarithmic Sobolev inequalities on the discrete cube, and Margulis' graph connectivity theorem, Geom. Funct. Anal. 3, No. 3 (1993), 295-314.