Heat kernels on non-compact riemannian manifolds : a partial survey
Séminaire de théorie spectrale et géométrie, Tome 15 (1996-1997), pp. 167-187. 
@article{TSG_1996-1997__15__167_0,
     author = {Thierry Coulhon},
     title = {Heat kernels on non-compact riemannian manifolds : a partial survey},
     journal = {S\'eminaire de th\'eorie spectrale et g\'eom\'etrie},
     pages = {167--187},
     publisher = {Institut Fourier},
     address = {Grenoble},
     volume = {15},
     year = {1996-1997},
     doi = {10.5802/tsg.189},
     zbl = {0903.58055},
     language = {en},
     url = {https://proceedings.centre-mersenne.org/articles/10.5802/tsg.189/}
}
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Thierry Coulhon. Heat kernels on non-compact riemannian manifolds : a partial survey. Séminaire de théorie spectrale et géométrie, Tome 15 (1996-1997), pp. 167-187. doi : 10.5802/tsg.189. https://proceedings.centre-mersenne.org/articles/10.5802/tsg.189/

[1] Bakry D., Coulhon T., Ledoux M., Saloff-Coste L. - Sobolev inequalities in disguise, Indiana Univ. Math. J., 44,4 ( 1995), 1033-1074. | Zbl

[2] Carey A., Coulhon T., Mathai V., Phillips J. - Von Neumann spectra near the spectral gap, to appear in Bull Sc. Math.. | MR | Zbl

[3] Carlen E., Kusuoka S., Stroock D. - Upper bounds for symmetric Markov transition fonctions, Ann. Inst.H.Poincaré, proba. et stat., suppl. au n° 2 ( 1987). 245-287. | Numdam | MR | Zbl

[4] Carron G. - Inégalités isopérimétriques sur les variétés riemanniennes, thesis, University of Grenoble, 1994.

[5] Carron G. - Inégalités isopérimétriques de Faber-Krahn et conséquences, in Actes de la table ronde de géométrie différentielle en l'honneur de Marcel Bergen Collection SMF Séminaires et congrès, n° 1( 1994), 205-232. | MR | Zbl

[6] Chavel I., Feldman E. - Modified isoperimetric constants and large time heat diffusion in Riemannian manifolds, Duke Math. J., 64, 3 ( 1991), 473-499. | MR | Zbl

[7] Coulhon T. - Dimension à l'infini d'un semi-groupe analytique, Bull Sc. Math., 2ème série, 114, 3 ( 1990), 485-500. | MR | Zbl

[8] Coulhon T. - Dimensions of continuous and discrete semigroups, in Semigroup theory and evolution equations, Clément, Mitidieri, De Pagter, éd., Marcel Dekker Lect. Notes in Pure and Appl. Math., vol.135 ( 1991), 93-99. | MR | Zbl

[9] Coulhon T. - Itération de Moser et estimation gaussienne du noyau de la chaleur, Jour. Oper. Th., 29 ( 1993), 157-165. | MR | Zbl

[10] Coulhon T. - Noyau de la chaleur et discrétisation d'une variété riemannienne, Israël J. Math., 80 ( 1992), 289-300. | MR | Zbl

[11] Coulhon T. - Espaces de Lipschitzet inégalités de Poincaré, J. Funct. Anal, 136,1 ( 1996), 81-113. | MR | Zbl

[12] Coulhon T. - Dimensions at infinity for Riemannian manifolds, Pot Anal, 4,4 ( 1995). 335-344. | MR | Zbl

[13] Coulhon T. - Ultracontractivity and Nash type inequalities. J. funct. Anal., 141, 2 ( 1996), 510-539. | MR | Zbl

[14] Coulhon T. - Analysis on infinite graphs with regular volume growth, to appear in Proceedings of the Cortona conference on random walks and discrete potential theory, 1997, Cambridge U.P. | MR | Zbl

[15] Coulhon T., Duong X.T. - Riesz transforms for 1 ≤ p ≤ 2, to appear in T.A.M.S.. | Zbl

[16] Coulhon T., Grigor'Yan A. - On-diagonal lower bounds for heat kernels and Markov chains, Duke Univ.Math. J., 89,1 ( 1997), 133-199. | MR | Zbl

[17] Coulhon T. - Grigor'Yan A., Random walks on graphs with regular volume growth, to appear in G.A.F.A. | MR | Zbl

[18] Coulhon T. - Grigor'Yan A., Manifolds with big heat kernels, preprint.

[19] Coulhon T., Koskela P. - Poincaré inequalities and Lp metrics, preprint, 1996.

[20] Coulhon T., Ledoux M. - Isopérimétrie, décroissance du noyau de la chaleur et transformations de Riesz: un conue-exemple, Arkiv für Mat., 32 ( 1994), 63-77. | MR | Zbl

[21] Coulhon T., Saloff-Coste L. - Isopérimétrie pour les groupes et les variétés, Rev. Mat. Iberoamer., 9, 2, ( 1993), 293-314. | MR | Zbl

[22] Coulhon T., Saloff-Coste L. - Variétés riemanniennes isométriques à l'infini, Rev. Mat. Iberoamer., 11,3 ( 1995), 687-726. | MR | Zbl

[23] Coulhon T., Saloff-Coste L. - Harnack inequality and hyperbolicity for the p-Laplacian with applications to Picard type theorems, preprint.

[24] Davies E.B. - Heat kernels and spectral theory,Cambridge University Press, 1989. | MR | Zbl

[25] Davies E.B. - Non-Gaussian aspects of heat kernel behaviour, J. London Math. Soc, 2, 55 ( 1995). 105-125. | MR | Zbl

[26] Davies E.B., Pang M. - Sharp heat kernel bounds for some Laplace operators, Quart, J. Math.Oxford, Ser. 2, 40 ( 1989), 281-290,. | MR | Zbl

[27] Delin H. - A proof of the equivalence between Nash and Sobolev inequality, Bull. Sc. Math., 120 ( 1996), 405-411. | MR | Zbl

[28] Duong X.Mcintosh A., Singular integral operators with non-smooth kernels on irregular domains, preprint. | MR

[29] Grigor'Yan A. - The heat equation on non-compact Riemannian manifolds, in Ru ssi an: Matem. Sbornik, 182,1,55-87, 1991; English translation: Math. USSR Sb., 72,1 ( 1992), 47-77. | MR | Zbl

[30] Grigor'Yan A. - Heat kernel upper bounds on a complete non-compact manifold, Rev. Mat. Iberoamericana, 10, 2 ( 1994). 395-452. | MR | Zbl

[31] Grigor'Yan A. - Upper bounds of derivatives of the heat kernel on an arbitrary complete manifold, J. Funct. Anal., 127 ( 1995), 363-389. | MR | Zbl

[32] Grigor'Yan A. - Gaussian upper bounds for the heat kernel on arbitrary manifolds, J. Diff. Geom., 45 ( 1997), 33-52. | MR | Zbl

[33] Grigor'Yan A. - Heat kernel on a non-compact Riemannian manifold, in 1993 Summer research institute on stochastic analysis, ed. M. Pinsky et alia, Proceedings of Symposia in Pure Math., 57 ( 1994), 239-263. | MR | Zbl

[34] Grigor'Yan A. - Analytic and geometric background of recurrence and non-explosion of the brownian motion on Riemannian manifolds, preprint. | MR | Zbl

[35] Grigor'Yan A., Saloff-Coste L. - Heat kernel on manifolds with ends, preprint.

[36] Heinonen J., Koskela P. - Quasiconformal maps in metric spaces with controlled geometry, preprint, 1996. | MR | Zbl

[37] Kanai M. - Analytic inequalities, and rough isometries between non-compact Riemannian manifolds, in Curvature and Topology of Riemannian Manifolds, Springer Lecture Notes 1201 ( 1986), 122-137. | MR | Zbl

[38] Li P., Yau S.T. - On the parabolic kernel of the Schrödinger operator, Acta Math., 156 ( 1986), 153-201. | MR | Zbl

[39] Pittet C. - Folner séquences on polycyclic groups, Rev. Mat. Iberoamer, 11 ( 1995), 675-685. | MR | Zbl

[40] Pittet C., Saloff-Coste L. Amenable groups, isoperimetric profiles and random walks, preprint. | MR | Zbl

[41] Russ E. - Duals of Hp spaces on Riemannian manifolds and on graphs, preprint.

[42] Russ E. - H1-L1 boundedness for Riesz transforms on Riemannian manifolds and on graphs, preprint. | MR | Zbl

[43] Saloff-Coste L. - Uniformly elliptic operators on Riemannian manifolds, J. Diff. Geom. 36 ( 1992), 417-450. | MR | Zbl

[44] Saloff-Coste L. - A note on Poincaré, Sobolev, and Harnack inequalities, Duke Math. J., I.M.R.N., 2 ( 1992), 27-38. | MR | Zbl

[45] Saloff-Coste L. - On global Sobolev inequalities, Forum Mat., 6 ( 1994), 271-286. | MR | Zbl

[46] Saloff-Coste L. - Parabolic Harnack inequality for divergence form second order differential operators, Pot. Anal, 4,4 ( 1995), 429-467. | MR | Zbl

[47] Sikora A. - Sharp pointwise estimates on heat kernels, Quart.J. Math. Oxford, Ser. 2, 47 ( 1996), 371-382. | MR | Zbl

[48] Urakawa H. - Geometry of Laplace-Beltrami operator on a complete Riemannian manifold, in Progress in differential geometry, Advances Studies in Pure Math., Math. Soc. Japan, Tokyo, 22 ( 1993), 347-406. | MR | Zbl

[49] Varopoulos N. - Une généralisation du théorème de Hardy-Littlewood-Sobolev pour les espaces de Dirichlet, C.R.A.S Paris, 299, I ( 1984), 651-654. | MR | Zbl

[50] Varopoulos N. - Isoperimetric inequalities and Markov chains, J. Funct. Anal, 63, 2 ( 1985), 215-239. | MR | Zbl

[51] Varopoulos N. - Hardy-Littlewood theory for semigroups, J. Funct. Anal., 63, 2 ( 1985), 240-260. | MR | Zbl

[52] Varopoulos N. - Random walks and Brownian motion on manifolds, Symposia Math., XXIX { 1987), 97-109. | MR | Zbl

[53] Varopoulos N. - Analysis on Lie groups, J. Funct. Anal, 76, 2 ( 1988), 346-410. | MR | Zbl

[54] Varopoulos N. - Small time Gaussian estimates of heat diffusion kernels. Part I: the semigroup technique, Bull Sc. Math., 113 ( 1989), 253-277. | MR | Zbl

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