Compact manifolds with positive \(m\)-Bakry-Émery Ricci tensor

DOI10.1016/J.DIFGEO.2013.10.018zbMath1290.53062OpenAlexW2044167714WikidataQ115356425 ScholiaQ115356425MaRDI QIDQ389353

Hongcun Deng

Publication date: 20 January 2014

Published in: Differential Geometry and its Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.difgeo.2013.10.018

zbMATH Keywords

\(f\)-mean curvature\(f\)-minimal surface\(m\)-Bakry-Émery Ricci curvatureeigenvalue comparison

Mathematics Subject Classification ID

Differential geometry of immersions (minimal, prescribed curvature, tight, etc.) (53C42) Rigidity results (53C24) Methods of global Riemannian geometry, including PDE methods; curvature restrictions (53C21)

Related Items (1)

Harmonic Aspects in an $\eta$-Ricci Soliton

Cites Work

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• Generic mean curvature flow. I: Generic singularities
• Rigidity of quasi-Einstein metrics
• Extension of Reilly formula with applications to eigenvalue estimates for drifting Laplacians
• Two rigidity theorems on manifolds with Bakry-Emery Ricci curvature
• Comparison geometry for the Bakry-Emery Ricci tensor
• Asymptotic behavior for singularities of the mean curvature flow
• Vanishing sectional curvature on the boundary and a conjecture of Schroeder and Strake
• Eigenvalue comparison theorems and its geometric applications
• Rigidity and sphere theorem for manifolds with positive Ricci curvature
• Sobolev inequalities and Myers's diameter theorem for an abstract Markov generator
• \(f\)-minimal surface and manifold with positive \(m\)-Bakry-Émery Ricci curvature
• Stable weighted minimal surfaces in manifolds with non-negative Bakry-Emery Ricci tensor

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