The structure of weakly stable constant mean curvature hypersurfaces
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Publication:925100
DOI10.2748/tmj/1206734408zbMath1154.53036OpenAlexW2127734132MaRDI QIDQ925100
Xu Cheng, Leung-Fu Cheung, Detang Zhou
Publication date: 29 May 2008
Published in: Tôhoku Mathematical Journal. Second Series (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.2748/tmj/1206734408
Differential geometry of immersions (minimal, prescribed curvature, tight, etc.) (53C42) Methods of global Riemannian geometry, including PDE methods; curvature restrictions (53C21)
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Cites Work
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- On the oriented Plateau problem
- Stability of hypersurfaces with constant mean curvature
- On complete minimal surfaces with finite Morse index in three manifolds
- Stability of complete noncompact surfaces with constant mean curvature
- Stability of hypersurfaces of constant mean curvature in Riemannian manifolds
- On the compactness of constant mean curvature hypersurfaces with finite total curvature
- Harmonic functions and the structure of complete manifolds
- Harmonic maps and the topology of stable hypersurfaces and manifolds with non-negative Ricci curvature
- The structure of stable minimal hypersurfaces in \(\mathbb{R}^{n+1}\)
- Minimal hypersurfaces with finite index
- On stable minimal surfaces in manifolds of positive bi-Ricci curvatures
- On constant mean curvature hypersurfaces with finite index
- 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
- The splitting theorem for manifolds of nonnegative Ricci curvature
- 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
- Differential equations on riemannian manifolds and their geometric applications
- Stable complete surfaces with constant mean curvature
- Stable minimal hypersurfaces in a nonnegatively curved manifold
- L 2 harmonic forms and stability of hypersurfaces with constant mean curvature
- The structure of weakly stable minimal hypersurfaces