Upper bounds on the first eigenvalue for a diffusion operator via Bakry-Émery Ricci curvature

DOI10.1016/J.JMAA.2009.09.019zbMath1183.58028OpenAlexW2059392945MaRDI QIDQ1036151

Jia-Yong Wu

Publication date: 5 November 2009

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jmaa.2009.09.019

zbMATH Keywords

Dirichlet formeigenvalue estimatediffusion operatorBakry-Emery Ricci curvature

Mathematics Subject Classification ID

Spectral problems; spectral geometry; scattering theory on manifolds (58J50)

Related Items (17)

Eigenvalues of the drifting Laplacian on complete noncompact Riemannian manifolds ⋮ Upper bounds on the first eigenvalue for a diffusion operator via Bakry-Émery Ricci curvature. II ⋮ ESTIMATES FOR THE EIGENVALUES OF THE DRIFTING LAPLACIAN ON SOME COMPLETE RICCI SOLITONS ⋮ Upper bounds on the first eigenvalue for the \(p\)-Laplacian ⋮ Heat kernel estimate for the Laplace-Beltrami operator under Bakry-Émery Ricci curvature condition and applications ⋮ A note on the splitting theorem for the weighted measure ⋮ Intrinsic and extrinsic comparison results for isoperimetric quotients and capacities in weighted manifolds ⋮ The logarithmic entropy formula for the linear heat equation on Riemannian manifolds ⋮ Gradient estimates for a simple parabolic Lichnerowicz equation ⋮ \(L^p\)-Liouville theorems on complete smooth metric measure spaces ⋮ De Lellis-Topping type inequalities for smooth metric measure spaces ⋮ Global lower bounds on the first eigenvalue for a diffusion operator ⋮ Rigidity of manifolds with Bakry-Émery Ricci curvature bounded below ⋮ On Ricci-harmonic metrics ⋮ The first eigenvalue of Witten-Laplacian on manifolds with time-dependent metrics ⋮ Eigenvalues of the drifting Laplacian on smooth metric measure spaces ⋮ Convergence of harmonic maps

Cites Work

• An extension of E. Hopf's maximum principle with an application to Riemannian geometry
• Harnack inequality and Liouville properties for \(L\)-harmonic operator
• Eigenvalue comparison theorems and its geometric applications
• Harnack inequalities on a manifold with positive or negative Ricci curvature
• Some geometric properties of the Bakry-Émery-Ricci tensor
• Some new results on eigenvectors via dimension, diameter, and Ricci curvature
• Lévy-Gromov's isoperimetric inequality for an infinite dimensional diffusion generator
• On the geometry of metric measure spaces. I
• On the geometry of metric measure spaces. II
• Liouville theorems for symmetric diffusion operators on complete Riemannian manifolds
• Differential equations on riemannian manifolds and their geometric applications
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