Stable hypersurfaces with constant scalar curvature

Alencar, Hilário; Santos, Walcy; Zhou, Detang

doi:10.1090/S0002-9939-10-10388-8

Stable hypersurfaces with constant scalar curvature
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by Hilário Alencar, Walcy Santos and Detang Zhou

Proc. Amer. Math. Soc. 138 (2010), 3301-3312

DOI: https://doi.org/10.1090/S0002-9939-10-10388-8

Published electronically: April 22, 2010

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Abstract:

We obtain some nonexistence results for complete noncompact stable hypersurfaces 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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