Stable hypersurfaces with constant scalar curvature in Euclidean spaces

2009/09/10 by Hilário Alencar, Alencar, Hilário, Walcy Santos +3
Mathematics · Physics and Astronomy · #Advanced Differential Geometry Research #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #math.DG #msc:53C42

paper · pdf · doi:10.48550/arxiv.0909.2042

arxiv created 2009/09/10 · arxiv updated 2009/12/01

Abstract

We obtain some nonexistence results for complete noncompact stable hyppersurfaces with nonnegative constant scalar curvature in Euclidean spaces. As a special case we prove that there is no complete noncompact strongly stable hypersurface M in ℝ⁴ with zero scalar curvature S₂, nonzero Gauss-Kronecker curvature and finite total curvature (i.e. ∫_M|A|³<+∞).

Citations

• Curvature integral estimates for complete hypersurfaces

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