Rigidity of manifolds with Bakry-Émery Ricci curvature bounded below

DOI10.1007/s10711-011-9685-xzbMath1257.53064OpenAlexW2170148207MaRDI QIDQ715185

Yan-Hui Su, Hui-Chun Zhang

Publication date: 2 November 2012

Published in: Geometriae Dedicata (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10711-011-9685-x

zbMATH Keywords

spectrumBakry-Émery Ricci curvaturesplitting type theorem

Mathematics Subject Classification ID

Spectral problems; spectral geometry; scattering theory on manifolds (58J50) Rigidity results (53C24)

Related Items (9)

Eigenvalues of the drifting Laplacian on complete noncompact Riemannian manifolds ⋮ Some upper estimates on the bottom spectrum of Finsler measure spaces ⋮ 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 ⋮ Prescribing curvature problem of Bakry-Émery Ricci tensor ⋮ Eigenvalue estimates for Beltrami-Laplacian under Bakry-Émery Ricci curvature condition ⋮ Heat kernel estimate for the Laplace-Beltrami operator under Bakry-Émery Ricci curvature condition and applications ⋮ Prescribing curvature problems on the Bakry-Emery Ricci tensor of a compact manifold with boundary ⋮ \(L^p\)-Liouville theorems on complete smooth metric measure spaces

Cites Work

• Unnamed Item
• Smooth metric measure spaces with non-negative curvature
• Comparison geometry for the Bakry-Emery Ricci tensor
• Weak curvature conditions and functional inequalities
• The upper bound of the \({{\text L}_{\mu}^2}\) spectrum
• Upper bounds on the first eigenvalue for a diffusion operator via Bakry-Émery Ricci curvature
• Eigenvalue comparison theorems and its geometric applications
• Some new results on eigenvectors via dimension, diameter, and Ricci curvature
• Complete manifolds with positive spectrum
• Complete manifolds with positive spectrum. II.
• On the geometry of metric measure spaces. II
• Liouville theorems for symmetric diffusion operators on complete Riemannian manifolds
• Ends of locally symmetric spaces with maximal bottom spectrum
• Analysis on local Dirichlet spaces. I. Recurrence, conservativeness and Lp-Liouville properties.

This page was built for publication: Rigidity of manifolds with Bakry-Émery Ricci curvature bounded below