Abstract
In this paper, we show that all complete stable hypersurfaces in ℝ n+1(or ℍ n+1 (-1)) (n = 3, 4, 5) with constant mean curvature H > 0 (or H > 1, respectively) and finite L 2 norm of traceless second fundamental form are compact geodesic spheres. Keywords: stable hypersurface, constant mean curvature, isometric immersion, Bernstein theorem.
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