Rigidity of complete spacelike hypersurfaces with constant weighted mean curvature

DOI10.1007/s13366-015-0253-7zbMath1356.53064OpenAlexW629983935MaRDI QIDQ304549

Márcio S. Santos, Arlandson Matheus Silva Oliveira, Henrique Fernandes de Lima

Publication date: 25 August 2016

Published in: Beiträge zur Algebra und Geometrie (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s13366-015-0253-7

zbMATH Keywords

Bakry-Émery-Ricci tensordrifting Laplacian\(f\)-mean curvaturecomplete space-like hypersurfacesentire space-like graphsweighted Lorentzian product spaces

Mathematics Subject Classification ID

Higher-dimensional and -codimensional surfaces in Euclidean and related (n)-spaces (53A07) Estimates of eigenvalues in context of PDEs (35P15) Differential geometry of immersions (minimal, prescribed curvature, tight, etc.) (53C42) Global differential geometry of Lorentz manifolds, manifolds with indefinite metrics (53C50)

Related Items (5)

Spacelike hypersurfaces in weighted generalized Robertson-Walker space-times ⋮ New Calabi-Bernstein type results in Lorentzian product spaces with density ⋮ Some maximum principles for the drift Laplacian applied to complete spacelike hypersurfaces ⋮ Spacelike translating solitons of the mean curvature flow in Lorentzian product spaces with density ⋮ Rigidity of complete spacelike hypersurfaces in spatially weighted generalized Robertson-Walker spacetimes

Cites Work

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• Parabolicity of maximal surfaces in Lorentzian product spaces
• Stability properties and topology at infinity of \(f\)-minimal hypersurfaces
• Graphic Bernstein results in curved pseudo-Riemannian manifolds
• Comparison geometry for the Bakry-Emery Ricci tensor
• New examples of entire maximal graphs in \(\mathbb H^2 \times \mathbb R_1\)
• Calabi-Bernstein results for maximal surfaces in Lorentzian product spaces
• Entire spacelike hypersurfaces of constant mean curvature in Minkowski space
• Maximal space-like hypersurfaces in the Lorentz-Minkowski spaces
• Isoperimetry of waists and concentration of maps
• On the curvatures of bounded complete spacelike hypersurfaces in the Lorentz-Minkowski space
• Singularity theorems and the Lorentzian splitting theorem for the Bakry-Emery-Ricci tensor
• Generalized maximum principles and the unicity of complete spacelike hypersurfaces immersed in a Lorentzian product space
• Spacelike graphs with parallel mean curvature
• Variétés kählériennes à première classe de Chern non negative et variétés riemanniennes à courbure de Ricci généralisée non negative. (Kählerian manifolds of non-negative first Chern class and Riemannian manifolds with non-negative generalized Ricci curvature)
• Harmonic forms on manifolds with non-negative Bakry-Émery-Ricci curvature
• Uniqueness of spacelike hypersurfaces with constant higher order mean curvature in generalized Robertson–Walker spacetimes

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