Complete hypersurfaces with constant scalar curvature in a hyperbolic space.
Shu, Shichang (2007)
Balkan Journal of Geometry and its Applications (BJGA)
Similarity:
Shu, Shichang (2007)
Balkan Journal of Geometry and its Applications (BJGA)
Similarity:
Bo Guan, Joel Spruck (2010)
Journal of the European Mathematical Society
Similarity:
This is the second of a series of papers in which we investigate the problem of finding, in hyperbolic space, complete hypersurfaces of constant curvature with a prescribed asymptotic boundary at infinity for a general class of curvature functions. In this paper we focus on graphs over a domain with nonnegative mean curvature.
Yoshihiro Tonegawa (1996)
Mathematische Zeitschrift
Similarity:
Julian Scheuer (2015)
Geometric Flows
Similarity:
We prove gradient estimates for hypersurfaces in the hyperbolic space Hn+1, expanding by negative powers of a certain class of homogeneous curvature functions F. We obtain optimal gradient estimates for hypersurfaces evolving by certain powers p > 1 of F-1 and smooth convergence of the properly rescaled hypersurfaces. In particular, the full convergence result holds for the inverse Gauss curvature flow of surfaces without any further pinching condition besides convexity of the initial...
Bang-Yen Chen (2002)
Archivum Mathematicum
Similarity:
First we prove a general algebraic lemma. By applying the algebraic lemma we establish a general inequality involving the Ricci curvature of an arbitrary real hypersurface in a complex hyperbolic space. We also classify real hypersurfaces with constant principal curvatures which satisfy the equality case of the inequality.
João Lucas Marques Barbosa, Ricardo Sa Earp (1997-1998)
Séminaire de théorie spectrale et géométrie
Similarity:
de Lima, Henrique F., de Lima, Joseilson R. (2009)
International Journal of Mathematics and Mathematical Sciences
Similarity:
Qing-Ming Cheng (1994)
Manuscripta mathematica
Similarity:
Cícero P. Aquino, Henrique F. de Lima, Fábio R. dos Santos (2016)
Colloquium Mathematicae
Similarity:
We deal with complete spacelike hypersurfaces immersed with constant mean curvature in a Lorentzian space form. Under the assumption that the support functions with respect to a fixed nonzero vector are linearly related, we prove that such a hypersurface must be either totally umbilical or isometric to a hyperbolic cylinder of the ambient space.
Barbara Nelli, Harold Rosenberg (1997)
Annales de l'institut Fourier
Similarity:
We consider graphs of positive scalar or Gauss-Kronecker curvature over a punctured disk in Euclidean and hyperbolic -dimensional space and we obtain removable singularities theorems.