메뉴 건너뛰기




Volumn 7, Issue 3, 2003, Pages 203-224

The Gaussian Isoperimetric Inequality and Transportation

Author keywords

Isoperimetric function; Logarithmic Sobolev inequality; Orlicz spaces; Transportation

Indexed keywords


EID: 1642581772     PISSN: 13851292     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1026242611940     Document Type: Article
Times cited : (19)

References (28)
  • 1
    • 0030533361 scopus 로고    scopus 로고
    • Lévy-Gromov's isoperimetric inequality for an infinite dimensional diffusion generator
    • Bakry, D. and Ledoux, M.: Lévy-Gromov's isoperimetric inequality for an infinite dimensional diffusion generator, Invent. Math. 123 (1996), 259-281.
    • (1996) Invent. Math. , vol.123 , pp. 259-281
    • Bakry, D.1    Ledoux, M.2
  • 2
    • 0033233673 scopus 로고    scopus 로고
    • Isoperimetric and analytic inequalities for log-concave probability measures
    • Bobkov, S.G.: Isoperimetric and analytic inequalities for log-concave probability measures, Annals Probab. 27 (1999), 1903-1921.
    • (1999) Annals Probab. , vol.27 , pp. 1903-1921
    • Bobkov, S.G.1
  • 3
    • 0002829137 scopus 로고    scopus 로고
    • Exponential integrability and transportation cost related to logarithmic Sobolev inequalities
    • Bobkov, S.G. and Götze, F.: Exponential integrability and transportation cost related to logarithmic Sobolev inequalities, J. Funct. Anal. 162 (1999), 1-28.
    • (1999) J. Funct. Anal. , vol.162 , pp. 1-28
    • Bobkov, S.G.1    Götze, F.2
  • 4
    • 0035638785 scopus 로고    scopus 로고
    • Hypercontractivity of Hamilton-Jacobi equations
    • Bobkov, S.G., Gentil I. and Ledoux, M.: Hypercontractivity of Hamilton-Jacobi equations, J. Math. Pures Appl. (9) 80 (2001), 669-696.
    • (2001) J. Math. Pures Appl. , vol.80 , Issue.9 , pp. 669-696
    • Bobkov, S.G.1    Gentil, I.2    Ledoux, M.3
  • 5
    • 0034553975 scopus 로고    scopus 로고
    • From Brunn-Minkowski to Brescamp-Lieb and to logarithmic Sobolev inequalities
    • Bobkov, S.G. and Ledoux, M.: From Brunn-Minkowski to Brescamp-Lieb and to logarithmic Sobolev inequalities, Geometric and Funct. Anal. 10 (2000), 1028-1052.
    • (2000) Geometric and Funct. Anal. , vol.10 , pp. 1028-1052
    • Bobkov, S.G.1    Ledoux, M.2
  • 6
    • 0001639899 scopus 로고
    • The Brunn-Minkowski inequality in Gauss space
    • Borell, C.: The Brunn-Minkowski inequality in Gauss space, Invent. Math. 30 (1975), 207-216.
    • (1975) Invent. Math. , vol.30 , pp. 207-216
    • Borell, C.1
  • 7
    • 84990623199 scopus 로고
    • Polar factorization and monotone rearrangement of vector-valued functions
    • Brenier, Y.: Polar factorization and monotone rearrangement of vector-valued functions, Comm. Pure. Appl. Math. 44 (1991), 375-417.
    • (1991) Comm. Pure. Appl. Math. , vol.44 , pp. 375-417
    • Brenier, Y.1
  • 8
    • 84968482174 scopus 로고
    • The regularity of mappings with a convex potential
    • Caffarelli, L.A.: The regularity of mappings with a convex potential, J. Amr. Math. Soc. 5 (1992), 99-104.
    • (1992) J. Amr. Math. Soc. , vol.5 , pp. 99-104
    • Caffarelli, L.A.1
  • 9
    • 0002356751 scopus 로고
    • Strict entropy production bounds and stability of the rate of convergence to equilibrium for the Boltzmann equation
    • Carlen, E.A. and Carvallo, M.C.: Strict entropy production bounds and stability of the rate of convergence to equilibrium for the Boltzmann equation, J. Statist. Phys. 67 (1992), 575-608.
    • (1992) J. Statist. Phys. , vol.67 , pp. 575-608
    • Carlen, E.A.1    Carvallo, M.C.2
  • 11
    • 38249018162 scopus 로고
    • Hypercontractivity and spectral gap of symmetric diffusions with applications to the stochastic Ising models
    • Deuschel, J.-D. and Stroock, D.W.: Hypercontractivity and spectral gap of symmetric diffusions with applications to the stochastic Ising models, J. Funct. Anal. 92 (1990), 30-48.
    • (1990) J. Funct. Anal. , vol.92 , pp. 30-48
    • Deuschel, J.-D.1    Stroock, D.W.2
  • 14
    • 0001103156 scopus 로고    scopus 로고
    • The geometry of optimal transportation
    • Gangbo, W. and McCann, R.J.: The geometry of optimal transportation, Acta Math. 177 (1996), 113-161.
    • (1996) Acta Math. , vol.177 , pp. 113-161
    • Gangbo, W.1    McCann, R.J.2
  • 15
    • 0009389702 scopus 로고
    • Isoperimetric inequalities in Riemannian manifolds
    • Appendix; V.D. Milman and G. Schechtman, (eds) Springer Lecture Notes in Mathematics, Springer, Berlin
    • Gromov, M.: Isoperimetric inequalities in Riemannian manifolds, Appendix pp. 114-129; in V.D. Milman and G. Schechtman, (eds) Asymptotic Theory of Finite Dimensional Normed Spaces, Springer Lecture Notes in Mathematics 1200, Springer, Berlin, 1986.
    • (1986) Asymptotic Theory of Finite Dimensional Normed Spaces , vol.1200 , pp. 114-129
    • Gromov, M.1
  • 16
    • 0001429116 scopus 로고
    • Logarithmic Sobolev inequalities
    • Gross, L.: Logarithmic Sobolev inequalities, Amr. J. Math. 97 (1975), 1061-1083.
    • (1975) Amr. J. Math. , vol.97 , pp. 1061-1083
    • Gross, L.1
  • 17
    • 0037740749 scopus 로고
    • Semigroup proofs of the isoperimetric inequality in Euclidean and Gauss space
    • Ledoux, M.: Semigroup proofs of the isoperimetric inequality in Euclidean and Gauss space, Bull. Sci. Math. 118 (1994), 485-510.
    • (1994) Bull. Sci. Math. , vol.118 , pp. 485-510
    • Ledoux, M.1
  • 18
    • 0001525416 scopus 로고
    • A simple analytic proof of an inequality by P. Buser
    • Ledoux, M.: A simple analytic proof of an inequality by P. Buser, Proc. Amr. Math. Soc. 121 (1994), 951-959.
    • (1994) Proc. Amr. Math. Soc. , vol.121 , pp. 951-959
    • Ledoux, M.1
  • 19
    • 0002075128 scopus 로고
    • Isopérimétrie et inégalités de Sobolev logarithmiques gaussiennes
    • Ledoux, M.: Isopérimétrie et inégalités de Sobolev logarithmiques gaussiennes, C.R. Acad. Sci. Math. 306 (1988), 79-82.
    • (1988) C.R. Acad. Sci. Math. , vol.306 , pp. 79-82
    • Ledoux, M.1
  • 20
    • 0000458262 scopus 로고    scopus 로고
    • Séminaire de Probabilités XXXIII. Lecture Notes in Math., Springer, Berlin
    • Ledoux, M.: Concentration of Measure and Logarithmic Sobolev Inequalities, pp. 120-216 in Séminaire de Probabilités XXXIII. Lecture Notes in Math., 1709 Springer, Berlin 1999. (http://www-sv.cict.fr/lsp./Ledoux/).
    • (1999) Concentration of Measure and Logarithmic Sobolev Inequalities , vol.1709 , pp. 120-216
    • Ledoux, M.1
  • 23
    • 0031161793 scopus 로고    scopus 로고
    • A convexity principle for interacting gases
    • McCann, R.J.: A convexity principle for interacting gases, Adv. Math. 128 (1997), 153-179.
    • (1997) Adv. Math. , vol.128 , pp. 153-179
    • McCann, R.J.1
  • 24
    • 84974004014 scopus 로고
    • Existence and uniqueness of monotone measure-preserving maps
    • McCann, R.J.: Existence and uniqueness of monotone measure-preserving maps, Duke Math. J. 80 (1995), 309-323.
    • (1995) Duke Math. J. , vol.80 , pp. 309-323
    • McCann, R.J.1
  • 25
    • 0001559554 scopus 로고    scopus 로고
    • Generalizations of an inequality by Talagrand, and links with the logarithmic Sobolev inequality
    • Otto, F. and Villani, C.: Generalizations of an inequality by Talagrand, and links with the logarithmic Sobolev inequality, J. Funct. Anal. 173 (2000), 361-400.
    • (2000) J. Funct. Anal. , vol.173 , pp. 361-400
    • Otto, F.1    Villani, C.2
  • 26
    • 0002498629 scopus 로고
    • Molecular decompositions and embedding theorems for vector-valued Sobolev spaces with gradient norm
    • Pełczyński, A. and Wojciechowski, M.: Molecular decompositions and embedding theorems for vector-valued Sobolev spaces with gradient norm, Studia Math. 107 (1993), 61-100.
    • (1993) Studia Math. , vol.107 , pp. 61-100
    • Pełczyński, A.1    Wojciechowski, M.2
  • 27
    • 0002559316 scopus 로고
    • Extremal properties of half-spaces for spherically invariant measures
    • Sudakov, V.N. and Tsirel'son, B.S.: Extremal properties of half-spaces for spherically invariant measures, J. Soviet Math. 9 (1978), 9-18.
    • (1978) J. Soviet Math. , vol.9 , pp. 9-18
    • Sudakov, V.N.1    Tsirel'son, B.S.2
  • 28
    • 0030551055 scopus 로고    scopus 로고
    • Transportation cost for gaussian and other product measures
    • Talagrand, M.: Transportation cost for gaussian and other product measures, Geometric and Funct. Anal. 6 (1996), 587-600.
    • (1996) Geometric and Funct. Anal. , vol.6 , pp. 587-600
    • Talagrand, M.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.