Stable hypersurfaces with constant scalar curvature in Euclidean spaces

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 ${\mathbb{R}}^4$ with zero scalar curvature $S_2$, nonzero Gauss-Kronecker curvature and finite total curvature (i.e. ${\int }_M|A{|}^3<+\infty$).

References in corpus (1)

• Curvature integral estimates for complete hypersurfaces

Cited by in corpus (1)

• Curvature integral estimates for complete hypersurfaces