Total scalar curvature and rigidity of minimal hypersurfaces in Euclidean space

DOI10.1112/S0025579300014479zbMath1054.53078MaRDI QIDQ4435542

Gabjin Yun

Publication date: 16 November 2003

Published in: Mathematika (Search for Journal in Brave)

zbMATH Keywords

minimal surfacehyperplanetotal scalar curvature

Mathematics Subject Classification ID

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

Related Items

The complete hyper-surfaces with zero scalar curvature in \(\mathbb{R}^{n+1}\)

Cites Work

• Gap theorems for minimal submanifolds of Euclidean space
• Curvature estimates for minimal hypersurfaces
• The structure of stable minimal hypersurfaces in \(\mathbb{R}^{n+1}\)
• Finiteness of Index and Total Scalar Curvature for Minimal Hypersurfaces
• 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
• Sobolev and isoperimetric inequalities for riemannian submanifolds
• Sobolev and mean‐value inequalities on generalized submanifolds of Rⁿ