Some Bernstein-type rigidity theorems

DOI10.1016/j.jmaa.2011.12.013zbMath1235.53005OpenAlexW2071642201MaRDI QIDQ663746

Qiaoling Wang, Nilton Moura Barroso Neto

Publication date: 27 February 2012

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jmaa.2011.12.013

zbMATH Keywords

submanifoldsconstant mean curvatureminimalBernstein rigidity

Mathematics Subject Classification ID

Higher-dimensional and -codimensional surfaces in Euclidean and related (n)-spaces (53A07) Local submanifolds (53B25) Local differential geometry of Lorentz metrics, indefinite metrics (53B30)

Related Items (3)

Gap theorems for minimal submanifolds of a hyperbolic space ⋮ Rigidity of complete minimal hypersurfaces in a hyperbolic space ⋮ Rigidity and stability estimates for minimal submanifolds in the hyperbolic space

Cites Work

• Unnamed Item
• On the oriented Plateau problem
• Curvature estimates for minimal submanifolds of higher codimension
• Maximal spacelike submanifolds of a pseudo-Riemannian space of constant curvature
• Some interior regularity theorems for minimal surfaces and an extension of Bernstein's theorem
• Minimal varieties in Riemannian manifolds
• Minimal cones and the Bernstein problem
• On stable complete minimal hypersurfaces in R n +1
• The structure of complete stable minimal surfaces in 3-manifolds of non-negative scalar curvature
• Stable complete minimal surfaces in 𝑅³ are planes
• Differential equations on riemannian manifolds and their geometric applications
• On minimal submanifolds in an Euclidean space
• Bernstein-type theorems in hypersurfaces with constant mean curvature

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