Eigenvalue estimates for the weighted Laplacian on a Riemannian manifold

zbMath0922.58084MaRDI QIDQ1284622

Alberto G. Setti

Publication date: 10 October 1999

Published in: Rendiconti del Seminario Matematico della Università di Padova (Search for Journal in Brave)

Full work available at URL: http://www.numdam.org/item?id=RSMUP_1998__100__27_0

zbMATH Keywords

weight functionLaplace operatorRicci curvatureDirichlet formeigenvalue boundscomplete manifold

Mathematics Subject Classification ID

Estimates of eigenvalues in context of PDEs (35P15) Spectral problems; spectral geometry; scattering theory on manifolds (58J50)

Related Items (14)

Eigenvalue Estimates on Bakry–Émery Manifolds ⋮ Concentration, Ricci curvature, and eigenvalues of Laplacian ⋮ Eigenvalue inequalities for the buckling problem of the drifting Laplacian on Ricci solitons ⋮ Heinz mean curvature estimates in warped product spaces \(M\times _{e^{\psi }}N\) ⋮ Generalization of Philippin's results for the first Robin eigenvalue and estimates for eigenvalues of the bi-drifting Laplacian ⋮ Rigidity and gap results for low index properly immersed self-shrinkers in \(\mathbb{R}^{m + 1}\) ⋮ Eigenvalue estimates for Beltrami-Laplacian under Bakry-Émery Ricci curvature condition ⋮ Sobolev inequalities on a weighted Riemannian manifold of positive Bakry-Émery curvature and convex boundary ⋮ Spectral and stochastic properties of the \(f\)-Laplacian, solutions of PDEs at infinity and geometric applications ⋮ Diffusion-type operators, Liouville theorems and gradient estimates on complete manifolds ⋮ Eigenvalue estimates for a class of elliptic differential operators in divergence form ⋮ Nonlinear spectrums of Finsler manifolds ⋮ Leaps and bounds towards scale separation ⋮ Inequalities between Dirichlet, Neumann and buckling eigenvalues on Riemannian manifolds

Cites Work

• Hypercontractivity and spectral gap of symmetric diffusions with applications to the stochastic Ising models
• Analysis of the Laplacian on a complete Riemannian manifold
• Spectral geometry: direct and inverse problems. With an appendix by G. Besson
• On the spectrum of Cartan-Hadamard manifolds
• Eigenvalue comparison theorems and its geometric applications
• Heat kernel bounds, conservation of probability and the Feller property
• An upper bound to the spectrum of \(\Delta\) on a manifold of negative curvature
• Le spectre d'une variété riemannienne. (The spectrum of a Riemannian manifold)
• A Lower Bound for the Spectrum of the Laplacian in Terms of Sectional and Ricci Curvature
• Heat Kernel Bounds for Second Order Elliptic Operators on Riemannian Manifolds
• Exponential Growth and the Spectrum of the Laplacian
• Gaussian Estimates for the Heat Kernel of the Weighted Laplacian and Fractal Measures
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