Rigidity of entire graphs in weighted product spaces with nonnegative Bakry-Émery-Ricci tensor

DOI10.1515/ADVGEOM-2016-0024zbMath1386.53075OpenAlexW2554827048MaRDI QIDQ1707385

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

Publication date: 29 March 2018

Published in: Advances in Geometry (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1515/advgeom-2016-0024

zbMATH Keywords

entire graphsBakry-Émery-Ricci tensordrifting Laplacian\(f\)-mean curvatureGaussian spaceweighted product spaces\(f\)-parabolic graphs

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)

Related Items (5)

Uniqueness results and enclosure properties for hypersurfaces with boundary in weighted cylinders ⋮ Entire translating graphs in weighted product spaces: rigidity and nonexistence results ⋮ Two-sided hypersurfaces, entire Killing graphs and the mean curvature equation in warped products with density ⋮ Uniqueness of hypersurfaces in weighted product spaces via maximum principles for the drift Laplacian ⋮ Parabolicity criteria and characterization results for submanifolds of bounded mean curvature in model manifolds with weights

Cites Work

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• On the oriented Plateau problem
• Comparison geometry for the Bakry-Emery Ricci tensor
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• Two generalizations of Cheeger-Gromoll splitting theorem via Bakry-Emery Ricci curvature
• Isoperimetry of waists and concentration of maps
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• Minimal varieties in Riemannian manifolds
• Minimal cones and the Bernstein problem
• 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
• On Harnack's theorem for elliptic differential equations
• On S. Bernstein's Theorem on Surfaces z(x, y) of Nonpositive Curvature

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