[PDF] Top 20 Embedded positive constant r-mean curvature hypersurfaces in M

... Let M be an m-dimensional Riemannian manifold with sectional curvature bounded from ...consider hypersurfaces in the (m + 1)-dimensional product manifold M × R with ... See full document

... complete constant mean curvature spacelike hypersurfaces in the de Sitter space including the hyperbolic cylinders ([9] and [10]), so called because they can be generated by ...¯ ... See full document

... with positive constant r -mean curvature into a Riemannian product R × M n and whose boundary ∂
is contained into the slice {0} × M n (we note that Rosenberg [20] ... See full document

... oriented hypersurfaces M with constant mean curvature and two principal curvatures immersed in the Euclidean ...sphere. In the minimal case, Perdomo (Perdomo 2004) and ... See full document

... compact embedded surface S with constant mean curvature contained in an open hemisphere of S 3 must be a round ...⊂ R 3 , ρ −1 (T (r, a)) will be contained in an ... See full document

... surface in R 3 has finite index if and only if its total curvature is ...[G].) In fact, Fischer- Colbrie’s analysis allows us to obtain explicit estimates for the index of concrete examples ... See full document

... umbilical hypersurfaces and the curve shown there corresponds to the hyperbolic ...¯ R 6= 1, there is no complete hypersurface of the kind studied here and such that the corresponding point ( ¯ R, ... See full document

... do Carmo, M., Dajczer, M.: Necessary and sufficient conditions for existence of minimal hypersurfaces in spaces of constant curvature.. do Carmo, M., Dajczer, M.: Riemannia[r] ... See full document

... form R n+1 (1) for any m, 1 ≤ m ≤ n, and then, in [9], ...solutions. In the same paper [4], the authors also obtained C 0 and C 1 estimates for ... See full document

... appeared in [BE1] with the full results and a sketch of the ...[ET2]. In [NR] is solved the boundary-value problem for embedded hypersurfaces with constant mean curvature ... See full document

... when m = 1 (the mean curvature case), by V. Oliker [11] when m = n (the Gauss curvature case), and by ...< m < n. Other forms of such conditions for the Gauss ... See full document

... contained in one of the half spaces determined by the plane of the boundary, then the Alexandrov’s method of reflection (Alexandrov 1958) shows that M has all the symetries of its ...∂ M is a circle, ... See full document

... Let M n be a complete spacelike hypersurface with constant normalized scalar curvature R in the de Sitter Space S 1 n +1 ...the mean curvature and suppose that R = ... See full document

... boundary in IR 3 has finite index if and only if it is compact [LR], ...regions. In this paper, we prove, under some natural geometric conditions, that certain complete non-compact cmc hypersurfaces ... See full document

... that M and M ′ , as well as ∂M and ∂M ′ , are tangent at p ∈ ∂M ∩ ∂M ′ , with normal vectors pointing in the same ...that M and M ′ have r-mean ... See full document

... Let M be a compact Riemannian manifold with nonnegative Ricci curvature and o~, a codimension-one C3-foliation of M whose leaves have constant mean curvature.. Then [r] ... See full document

... [r] ... See full document

... Theorem 1 is the main theorem of this paper and goes a long way towards getting rid of condition (0.1) in Theorem B. For its proof we need an auxiliary proposition that might be interesting by itself and states ... See full document

... Interest in the study of spacelike hypersurfaces in Lorentzian manifolds has increased very much in recent years, from both the physical and mathematical points of ...spacelike ... See full document

... with constant mean curvature ...of constant higher order mean curvature, by applying the techniques used by Hoffman, de Lira and Rosenberg in [11], the second author ... See full document