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.
Publié le : 2010-05-15
Classification:
Stable hypersurface,
$L^2$ harmonic forms,
constant mean curvature,
harmonic map,
ends,
53C40,
58E20
@article{1287148618,
author = {Fu, Hai-Ping and Li, Zhen-Qi},
title = {On stable constant mean curvature hypersurfaces},
journal = {Tohoku Math. J. (2)},
volume = {62},
number = {1},
year = {2010},
pages = { 383-392},
language = {en},
url = {http://dml.mathdoc.fr/item/1287148618}
}
Fu, Hai-Ping; Li, Zhen-Qi. On stable constant mean curvature hypersurfaces. Tohoku Math. J. (2), Tome 62 (2010) no. 1, pp. 383-392. http://gdmltest.u-ga.fr/item/1287148618/