Foliations of Hyperbolic Space by Constant Mean Curvature Surfaces Sharing Ideal Boundary

Hyperbolic surfaces of $L_1$-2-type

In this paper, we show that an $L_1$-2-type surface in the three-dimensional hyperbolic space $H^3subset R^4_1$ either is an open piece of a standard Riemannian product $ H^1(-sqrt{1+r^2})times S^{1}(r)$, or it has non constant mean curvature, non constant Gaussian curvature, and non constant principal curvatures.

Constant curvature foliations in asymptotically hyperbolic spaces

Let (M, g) be an asymptotically hyperbolic manifold with a smooth conformal compactification. We establish a general correspondence between semilinear elliptic equations of scalar curvature type on ∂M and Weingarten foliations in some neighbourhood of infinity inM . We focus mostly on foliations where each leaf has constant mean curvature, though our results apply equally well to foliations whe...

Hypersurfaces with Constant Mean Curvature in a Lorentzian Space Form

On the Geometry of Constant Mean Curvature One Surfaces in Hyperbolic Space

We give a geometric classification of regular ends with constant mean curvature 1 and finite total curvature, embedded in hyperbolic space. We prove that each such end is either asymptotic to a catenoid cousin or asymptotic to a horosphere. We also study symmetry properties of constant mean curvature 1 surfaces in hyperbolic space associated to minimal surfaces in Euclidean space. We describe t...

On the k-nullity foliations in Finsler geometry

Here, a Finsler manifold $(M,F)$ is considered with corresponding curvature tensor, regarded as $2$-forms on the bundle of non-zero tangent vectors. Certain subspaces of the tangent spaces of $M$ determined by the curvature are introduced and called $k$-nullity foliations of the curvature operator. It is shown that if the dimension of foliation is constant, then the distribution is involutive...