Abstract
This article concerns the structure of complete noncompact stable hypersurfaces Mn with constant mean curvature H > 0 in a complete noncompact oriented Riemannian manifold Nn+1. In particular, we show that a complete noncompact stable constant mean curvature hypersurface Mn, n = 5, 6, in the Euclidean space must have only one end. Any such hypersurface in the hyperbolic space with, respectively, has only one end.
| Original language | English |
|---|---|
| Pages (from-to) | 161-190 |
| Number of pages | 30 |
| Journal | Annals of Global Analysis and Geometry |
| Volume | 36 |
| Issue number | 2 |
| DOIs | |
| Publication status | Published - 2009 Jul 1 |
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Keywords
- Constant mean curvature
- Hyperbolic space
- Nonparabolic end
- Parabolic end
- Stable hypersurface
ASJC Scopus subject areas
- Analysis
- Political Science and International Relations
- Geometry and Topology
Cite this
Stable complete noncompact hypersurfaces with constant mean curvature. / Chen, Jui-Tang.
In: Annals of Global Analysis and Geometry, Vol. 36, No. 2, 01.07.2009, p. 161-190.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Stable complete noncompact hypersurfaces with constant mean curvature
AU - Chen, Jui-Tang
PY - 2009/7/1
Y1 - 2009/7/1
N2 - This article concerns the structure of complete noncompact stable hypersurfaces Mn with constant mean curvature H > 0 in a complete noncompact oriented Riemannian manifold Nn+1. In particular, we show that a complete noncompact stable constant mean curvature hypersurface Mn, n = 5, 6, in the Euclidean space must have only one end. Any such hypersurface in the hyperbolic space with, respectively, has only one end.
AB - This article concerns the structure of complete noncompact stable hypersurfaces Mn with constant mean curvature H > 0 in a complete noncompact oriented Riemannian manifold Nn+1. In particular, we show that a complete noncompact stable constant mean curvature hypersurface Mn, n = 5, 6, in the Euclidean space must have only one end. Any such hypersurface in the hyperbolic space with, respectively, has only one end.
KW - Constant mean curvature
KW - Hyperbolic space
KW - Nonparabolic end
KW - Parabolic end
KW - Stable hypersurface
UR - http://www.scopus.com/inward/record.url?scp=70349456631&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=70349456631&partnerID=8YFLogxK
U2 - 10.1007/s10455-009-9155-y
DO - 10.1007/s10455-009-9155-y
M3 - Article
AN - SCOPUS:70349456631
VL - 36
SP - 161
EP - 190
JO - Annals of Global Analysis and Geometry
JF - Annals of Global Analysis and Geometry
SN - 0232-704X
IS - 2
ER -