Eigenvalue estimates for the weighted laplacian on a riemannian manifold
Rendiconti del Seminario Matematico della Università di Padova, Tome 100 (1998), pp. 27-55. 
@article{RSMUP_1998__100__27_0,
     author = {Setti, Alberto G.},
     title = {Eigenvalue estimates for the weighted laplacian on a riemannian manifold},
     journal = {Rendiconti del Seminario Matematico della Universit\`a di Padova},
     pages = {27--55},
     publisher = {Seminario Matematico of the University of Padua},
     volume = {100},
     year = {1998},
     mrnumber = {1675322},
     zbl = {0922.58084},
     language = {en},
     url = {http://www.numdam.org/item/RSMUP_1998__100__27_0/}
}
TY  - JOUR
AU  - Setti, Alberto G.
TI  - Eigenvalue estimates for the weighted laplacian on a riemannian manifold
JO  - Rendiconti del Seminario Matematico della Università di Padova
PY  - 1998
SP  - 27
EP  - 55
VL  - 100
PB  - Seminario Matematico of the University of Padua
UR  - http://www.numdam.org/item/RSMUP_1998__100__27_0/
LA  - en
ID  - RSMUP_1998__100__27_0
ER  - 
%0 Journal Article
%A Setti, Alberto G.
%T Eigenvalue estimates for the weighted laplacian on a riemannian manifold
%J Rendiconti del Seminario Matematico della Università di Padova
%D 1998
%P 27-55
%V 100
%I Seminario Matematico of the University of Padua
%U http://www.numdam.org/item/RSMUP_1998__100__27_0/
%G en
%F RSMUP_1998__100__27_0
Setti, Alberto G. Eigenvalue estimates for the weighted laplacian on a riemannian manifold. Rendiconti del Seminario Matematico della Università di Padova, Tome 100 (1998), pp. 27-55. http://www.numdam.org/item/RSMUP_1998__100__27_0/

[Au] T. Aubin, Non Linear Analysis on Manifolds. Monge-Ampère Equations, Springer-Verlag, New York (1982). | MR | Zbl

[bK] D. Bakry, Un critere de non-explosion pour certaines diffusions sur une variete'riemannienne complète, C.R. Acad. Sci. Paris, 303 (1986), pp. 23-26. | MR | Zbl

[3] D. Bakry, Etude des transformations de Riesz dans les variétés riemanniennes à courbure de Ricci minorée, in Séminaire de Probabilités XXI, Lecture Notes in Mathemetics, 1247, pp. 137-172, Springer-Verlag, Berlin, Heidelberg (1987). | Numdam | MR | Zbl

[BkE] D. Bakry - M. Emery, Diffusions hypercontractives, in Séminaire de Probabilites XIX, Lecture Notes in Mathemetics, 1123, pp. 179-206, Springer-Verlag, Berlin, Heidelberg (1985). | Numdam | MR | Zbl

[5] P. Berard, Spectral Geometry: Direct and Inverse Problems, Lecture Notes in Mathematics, 1207, Springer-Verlag, Berlin, Heidelberg (1986). | MR | Zbl

[BGM] M. Berger - P. Gauduchon - E. Mazet, Le spectre d'une variété Riemannienne, Lecture Notes in Methematics, 194, Springer-Verlag, Berlin, Heidelberg (1971). | MR | Zbl

[Br] R. Brooks, Exponential growth and the spectrum of the Laplacian, Proc. Amer. Math. Soc., 82 (1981), pp. 473-477. | MR | Zbl

[Cg] S.Y. Cheng, Eigenvalue comparison theorems and its geometric applications, Math. Z., 143 (1975), pp. 289-297. | MR | Zbl

[Cl] I. Chavel, Eigenvalues in Riemannian Geometry, Academic Press, Orlando (1984). | MR | Zbl

[Da1] E.B. Davies, Heat kernel bounds for second order elliptic operators on Riemannian manifolds, Amer. J. Math., 109 (1987), pp. 545-570. | MR | Zbl

[Da2] E.B. Davies, Heat Kernels and Spectral Theory, Cambridge University Press, Cambridge (1989). | MR | Zbl

[Da3] E.B. Davies, Heat kernel bounds, conservation of probability, and the Feller property, preprint. | MR | Zbl

[D1] J.D. Deuschel, On estimating the hypercontractive constant of a diffusion process on a compact manifold, preprint. | MR | Zbl

[DIS] J.D. Deuschel - D.W. Stroock, Hypercontractivity and spectral gap of symmetric diffusions with applications to the stochastic Ising model, J. Funct. Anal., 92 (1990), pp. 30-48. | MR | Zbl

[Hz] C. Herz, personal communication.

[Li] P. Li, Poincaré inequalities on Riemannian manifolds, in Seminar on Differential Geometry, Ann. Math. Stud., 102 (1982), pp. 73-84. | Zbl

[LiY] P. Li - S. T. YAU, Estimates of eigenvalues of a compact Riemannian manifold, Amer. Math. Soc. Proc. Symp. Pure Math., 36 (1980), pp. 205-240. | MR | Zbl

[Lz] A. Lichnerowicz, Géométrie des groupes de transformations, Dunod, Paris (1958). | MR | Zbl

[McK] H.P. Mckean, An upper bound for the spectrum of Δ on a manifold of negative curvature, J. Diff. Geom., 4 (1970), pp. 359-366. | Zbl

[ON] B. O'Neill, Semi-Riemannian Geometry. With Applicatios to Relativity, Academic Press, New York (1983). | MR | Zbl

[Pk] M. Pinsky, On the spectrum of Cartan-Hadamard manifolds, Pac. J. Math., 94 (1981), pp. 223-230. | MR | Zbl

[RSi] M. Reed - B. Simon, Methods of Modern Mathematical Physics. II. Fourier Analysis, Self adjointness, Academic Press, New York (1975). | MR | Zbl

[Se1] A.G. Setti, A lower bound for the spectrum of the Laplacian in terms of sectional and Ricci curvature, Proc. Amer. Math. Soc., 112 (1991), pp. 277-282. | MR | Zbl

[Se2] A.G. Setti, Gaussian estimates for the heat kernel of the weighted Laplacian and fractal measures, J. Canad. Math. Soc., 44 (1992), pp. 1061-1078. | MR | Zbl

[St] R.S. Strichartz, Analysis of the Laplacian on the complete Riemannian manifold, J. Funct. Anal., 52 (1983), pp. 48-79. | MR | Zbl