Remarks on the Rigidity and Stability of Minimal Submanifolds

DOI10.2307/2047437zbMath0672.53048OpenAlexW4234166972MaRDI QIDQ3825702

Makoto Sakaki

Publication date: 1989

Full work available at URL: https://doi.org/10.2307/2047437

zbMATH Keywords

second fundamental formLaplacianminimal immersionSimons type formula

Mathematics Subject Classification ID

Differential geometry of immersions (minimal, prescribed curvature, tight, etc.) (53C42)

Related Items (max. 100)

Nonexistence of some complete stable minimal submanifolds ⋮ Gauss curvature of Gaussian image of minimal surfaces ⋮ Normal curvature of minimal submanifolds in a sphere ⋮ Upper bounds for the index of minimal surfaces

Cites Work

• Stability of minimal surfaces and eigenvalues of the Laplacian
• Stability of minimal surfaces in a 3-dimensional hyperbolic space
• The area of the generalized Gaussian image and the stability of minimal surfaces in \(S^ n\) and \(R^ n\).
• Estimates on the stability of minimal surfaces and harmonic maps
• Minimal varieties in Riemannian manifolds
• Pinching Theorems of Simons Type for Complete Minimal Submanifolds in the Sphere
• Submanifolds with Constant Mean Curvature II
• Minimal Submanifolds of a Sphere with Second Fundamental Form of Constant Length

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