We study the global behavior of weakly stable constant mean curvature
hypersurfaces in a Riemannian manifold by using harmonic function theory. In
particular, a complete oriented weakly stable minimal hypersurface in the
Euclidean space must have only one end. Any complete noncompact weakly stable
hypersurface with constant mean curvature $H$ in the 4 and 5 dimensional
hyperbolic spaces has only one end under some restrictions on $H$.
Publié le : 2008-05-15
Classification:
hypersurfaces,
constant mean curvature,
harmonic function,
53C42,
53C21
@article{1206734408,
author = {Cheng, Xu and Cheung, Leung-fu and Zhou, Detang},
title = {The structure of weakly stable constant mean curvature hypersurfaces},
journal = {Tohoku Math. J. (2)},
volume = {60},
number = {1},
year = {2008},
pages = { 101-121},
language = {en},
url = {http://dml.mathdoc.fr/item/1206734408}
}
Cheng, Xu; Cheung, Leung-fu; Zhou, Detang. The structure of weakly stable constant mean curvature hypersurfaces. Tohoku Math. J. (2), Tome 60 (2008) no. 1, pp. 101-121. http://gdmltest.u-ga.fr/item/1206734408/