On Bernstein's problem of complete parabolic hypersurfaces in warped products

DOI10.1155/2023/6390463zbMath1525.53073OpenAlexW4381736178MaRDI QIDQ6048386

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Publication date: 10 October 2023

Published in: Advances in Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1155/2023/6390463

zbMATH Keywords

constant mean curvature surfaceswarped products

Mathematics Subject Classification ID

Differential geometry of immersions (minimal, prescribed curvature, tight, etc.) (53C42) General geometric structures on manifolds (almost complex, almost product structures, etc.) (53C15)

Cites Work

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• On Bernstein-type properties of complete hypersurfaces in weighted warped products
• On the rigidity of constant mean curvature complete vertical graphs in warped products
• On the oriented Plateau problem
• Complete vertical graphs with constant mean curvature in semi-Riemannian warped products
• Parabolicity and uniqueness of complete two-sided hypersurfaces immersed in a Riemannian warped product
• New Bernstein type results in weighted warped products
• Some interior regularity theorems for minimal surfaces and an extension of Bernstein's theorem
• Simple proofs of two theorems on minimal surfaces
• Minimal varieties in Riemannian manifolds
• Minimal cones and the Bernstein problem
• Rigidity of hypersurfaces and Moser-Bernstein type results in certain warped products, with applications to pseudo-hyperbolic spaces
• Unicity of constant mean curvature hypersurfaces in some riemannian manifolds
• CONSTANT MEAN CURVATURE HYPERSURFACES IN WARPED PRODUCT SPACES

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