Stable Constant Mean Curvature Hypersurfaces

  title={Stable Constant Mean Curvature Hypersurfaces},
  author={MARIA FERNANDA ELBERT and B. Nelli and Richard A. Wentworth},
Let Nn+1 be a Riemannian manifold with sectional curvatures uniformly bounded from below. When n = 3, 4, we prove that there are no complete (strongly) stable H-hypersurfaces, without boundary, provided |H| is large enough. In particular, we prove that there are no complete strongly stable H-hypersurfaces in Rn+1 without boundary, H = 0. 


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