Hilário Alencar, Walcy Santos, Detang Zhou
Published 2009-09-10Version 1
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 $\mathbb{R}^{4}$ with zero scalar curvature $S_2$, nonzero Gauss-Kronecker curvature and finite total curvature (i.e. $\int_M|A|^3<+\infty$).
Non-integrated defect relations for the Gauss map of a complete minimal surface with finite total curvature in $\mathbb R^m$
Complete hypersurfaces in Euclidean spaces with strong finite total curvature
On Generalized Spherical Surfaces in Euclidean Spaces
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