Abstract
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 homotopic 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.
Citation
Hai-Ping Fu. Zhen-Qi Li. "On stable constant mean curvature hypersurfaces." Tohoku Math. J. (2) 62 (3) 383 - 392, 2010. https://doi.org/10.2748/tmj/1287148618
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