On stable constant mean curvature hypersurfaces

摘要

We study complete non-compact stable constant mean curvature hypersurfaces in a Riemannian manifold of bounded geometry, and prove that there are no nontrivial L~2 harmonic 1-forms on such hypersurfaces. We also show that any smooth map with finite energy from such a hypersurface to a compact manifold with non-positive sectional curvature is nomotopic to constant on each compact set. In particular, we obtain some one-end theorems of complete non-compact weakly stable constant mean curvature hypersurfaces in the space forms.