@article{bwmeta1.element.bwnjournal-article-cmv67i1p109bwm,
author = {L. Saloff-Coste},
title = {Convergence to equilibrium and logarithmic Sobolev constant on manifolds with Ricci curvature bounded below},
journal = {Colloquium Mathematicae},
volume = {67},
year = {1994},
pages = {109-121},
zbl = {0816.53027},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-cmv67i1p109bwm}
}
Saloff-Coste, L. Convergence to equilibrium and logarithmic Sobolev constant on manifolds with Ricci curvature bounded below. Colloquium Mathematicae, Tome 67 (1994) pp. 109-121. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-cmv67i1p109bwm/
[000] [1] D. Aldous and P. Diaconis, Strong uniform times and finite random walks, Adv. Appl. Math. 8 (1987), 69-97.
[001] [2] D. Bakry, L'hypercontractivité et son utilisation en théorie des semigroupes, in: Ecole d'été de Saint Flour, 1992.
[002] [3] R. Brooks, On the spectrum of non-compact manifolds with finite volume, Math. Z. 187 (1984), 425-432. | Zbl 0537.58040
[003] [4] R. Brooks, The spectral geometry of tower of coverings, J. Differential Geom. 23 (1986), 97-107. | Zbl 0576.58033
[004] [5] R. Brooks, Combinatorial problems in spectral geometry, in: Lecture Notes in Math. 1201, Springer, 1988, 14-32.
[005] [6] P. Buser, B. Colbois and J. Dodziuk, Tubes and eigenvalues for negatively curved manifolds, J. Geom. Anal. 3 (1993), 1-26. | Zbl 0766.58054
[006] [7] J. Cheeger, M. Gromov and M. Taylor, Finite propagation speed, kernel estimates for functions of the Laplace operator, and the geometry of complete Riemannian manifolds, J. Differential Geom. 17 (1982), 15-53. | Zbl 0493.53035
[007] [8] S. Cheng, Eigenvalue comparison theorems and its geometric applications, Math. Z. 143 (1975), 289-297. | Zbl 0329.53035
[008] [9] Th. Coulhon et L. Saloff-Coste, Variétés Riemanniennes isométriques à l'infini, preprint, 1993.
[009] [10] J.-D. Deuschel and D. Stroock, Large Deviations, Academic Press, Boston, 1989.
[010] [11] P. Diaconis, Group Representations in Probability and Statistics, IMS, Hayward, CA, 1988.
[011] [12] P. Diaconis and L. Saloff-Coste, An application of Harnack inequality to random walk on finite nilpotent quotients, preprint, 1993. | Zbl 0889.60008
[012] [13] P. Diaconis and L. Saloff-Coste, Logarithmic Sobolev inequality for finite Markov chains, preprint, 1992.
[013] [14] M. Gromov, Groups of polynomial growth and expanding maps, Publ. IHES 53 (1980).
[014] [15] L. Gross, Logarithmic Sobolev inequalities, Amer. J. Math. 97 (1975), 1061-1083. | Zbl 0318.46049
[015] [16] R. Holley and D. Stroock, Uniform and convergence in one dimensional stochastic Ising models, Comm. Math. Phys. 123 (1989), 85-93. | Zbl 0666.60104
[016] [17] D. Kazhdan, Connection of the dual space of a group with the structure of its closed subgroups, Functional Anal. Appl. 1 (1968), 63-65. | Zbl 0168.27602
[017] [18] P. Li and S.-T. Yau, Estimates of eigenvalues of a compact Riemannian manifold, in: Proc. Sympos. Pure Math. 36, Amer. Math. Soc., 1980, 205-239.
[018] [19] P. Li and S.-T. Yau, On the parabolic kernel of the Schrödinger operator, Acta Math. 156 (1986), 153-201.
[019] [20] A. Lubotzky, Discrete Groups, Expanding Graphs and Invariant Measures, forthcoming monograph.
[020] [21] L. Payne and H. Weinberger, An optimal Poincaré inequality for convex domains, Arch. Rational Mech. Anal. 5 (1960), 286-292. | Zbl 0099.08402
[021] [22] O. Rothaus, Diffusion on compact Riemannian manifolds and logarithmic Sobolev inequalities, J. Funct. Anal. 42 (1981), 102-109. | Zbl 0471.58027
[022] [23] O. Rothaus, Hypercontractivity and the Bakry-Emery criterion for compact Lie groups, ibid. 65 (1986), 358-367. | Zbl 0589.58036
[023] [24] L. Saloff-Coste, Uniformly elliptic operators on Riemannian manifolds, J. Differential Geom. 36 (1992), 417-450. | Zbl 0735.58032
[024] [25] L. Saloff-Coste, A note on Poincaré, Sobolev and Harnack inequalities, Duke Math. J. 65 (1992), IMRN, 27-38. | Zbl 0769.58054
[025] [26] L. Saloff-Coste, Quantitative bounds on the convergence of diffusion semigroups to equilibrium, Math. Z., to appear. | Zbl 1059.43006
[026] [27] P. Sarnack, Some Applications of Modular Forms, Cambridge University Press, 1991.
[027] [28] D. Stroock and B. Zegarlinski, The equivalence of the logarithmic Sobolev inequality and the Dobrushin-Shlosman mixing condition, Comm. Math. Phys. 144 (1992), 303-323. | Zbl 0745.60104
[028] [29] N. Varopoulos, Une généralisation du théorème de Hardy-Littlewood-Sobolev pour les espaces de Dirichlet, C. R. Acad. Sci. Paris Sér. I 299 (1984), 651-654. | Zbl 0566.31006
[029] [30] N. Varopoulos, L. Saloff-Coste and Th. Coulhon, Analysis and Geometry on Groups, Cambridge University Press, 1993. | Zbl 1179.22009