Stable hypersurfaces with constant scalar curvature in Euclidean spaces

Details Stable hypersurfaces with constant scalar curvature in Euclidean spaces Stable hypersurfaces with constant scalar curvature in Euclidean spaces

2009-09-10

arxiv.org/abs/0909.2042v1

Mathematics

Differential Geometry

Scientific paper

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. $\int_M|A|^3<+\infty$).

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