@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] Non Linear Analysis on Manifolds. Monge-Ampère Equations, Springer-Verlag, New York (1982). | MR | Zbl
,[bK] 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] 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] Diffusions hypercontractives, in Séminaire de Probabilites XIX, Lecture Notes in Mathemetics, 1123, pp. 179-206, Springer-Verlag, Berlin, Heidelberg (1985). | Numdam | MR | Zbl
- ,[5] Spectral Geometry: Direct and Inverse Problems, Lecture Notes in Mathematics, 1207, Springer-Verlag, Berlin, Heidelberg (1986). | MR | Zbl
,[BGM] Le spectre d'une variété Riemannienne, Lecture Notes in Methematics, 194, Springer-Verlag, Berlin, Heidelberg (1971). | MR | Zbl
- - ,[Br] Exponential growth and the spectrum of the Laplacian, Proc. Amer. Math. Soc., 82 (1981), pp. 473-477. | MR | Zbl
,[Cg] Eigenvalue comparison theorems and its geometric applications, Math. Z., 143 (1975), pp. 289-297. | MR | Zbl
,[Cl] Eigenvalues in Riemannian Geometry, Academic Press, Orlando (1984). | MR | Zbl
,[Da1] Heat kernel bounds for second order elliptic operators on Riemannian manifolds, Amer. J. Math., 109 (1987), pp. 545-570. | MR | Zbl
,[Da2] Heat Kernels and Spectral Theory, Cambridge University Press, Cambridge (1989). | MR | Zbl
,[Da3] Heat kernel bounds, conservation of probability, and the Feller property, preprint. | MR | Zbl
,[D1] On estimating the hypercontractive constant of a diffusion process on a compact manifold, preprint. | MR | Zbl
,[DIS] 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] personal communication.
,[Li] Poincaré inequalities on Riemannian manifolds, in Seminar on Differential Geometry, Ann. Math. Stud., 102 (1982), pp. 73-84. | Zbl
,[LiY] 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] Géométrie des groupes de transformations, Dunod, Paris (1958). | MR | Zbl
,[McK] An upper bound for the spectrum of Δ on a manifold of negative curvature, J. Diff. Geom., 4 (1970), pp. 359-366. | Zbl
,[ON] Semi-Riemannian Geometry. With Applicatios to Relativity, Academic Press, New York (1983). | MR | Zbl
,[Pk] On the spectrum of Cartan-Hadamard manifolds, Pac. J. Math., 94 (1981), pp. 223-230. | MR | Zbl
,[RSi] Methods of Modern Mathematical Physics. II. Fourier Analysis, Self adjointness, Academic Press, New York (1975). | MR | Zbl
- ,[Se1] 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] 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] Analysis of the Laplacian on the complete Riemannian manifold, J. Funct. Anal., 52 (1983), pp. 48-79. | MR | Zbl
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