Displaying similar documents to “Complete hypersurfaces with constant scalar curvature in a hyperbolic space.”

Hypersurfaces of constant curvature in hyperbolic space II

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.

Ricci curvature of real hypersurfaces in complex hyperbolic space

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.

Gradient estimates for inverse curvature flows in hyperbolic space

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...