Stable complete noncompact hypersurfaces with constant mean curvature
This paper concerns the structure of complete noncompact stable hypersurfaces \(M^{n}\) with constant mean curvature \(H > 0\) in a complete noncompact oriented Riemannian manifold \(N^{n+1}\). In particular, the author shows that a complete noncompact stable constant mean curvature hypersurface \(M^{n },\;n = 5, 6\), in the Euclidean space must have only one end. Any such hypersurface in the hyperbolic space with \(H^{2} > \frac{65}{63},\frac{175}{148},\frac{41}{25},\frac{671}{171}\), for \(n=3,4,5,6\), respectively, has only one end.
scientific article; zbMATH DE number 5602560
scientific article