The shear-free condition and constant-mean-curvature hyperboloidal initial data

Construction of Hyperboloidal Initial Data

Let (M,g,Ω) be the conformal rescaling of a 3+1 dimensional vacuum spacetime (M̃, g̃), with g = Ωg̃, where Ω is a smooth function on M vanishing on the boundary ∂M. If M has smooth null boundary I , with connected components of topology S2×R, it follows that the Weyl tensor of (M,g) vanishes on I . From this follows peeling properties for (M̃, g̃). This picture of isolated systems in general relativ...

Hypersurfaces with Constant Mean Curvature in a Lorentzian Space Form

New Constant Mean Curvature Surfaces

We use the DPW construction [5] to present three new classes of immersed CMC cylinders, each of which includes surfaces with umbilics. The first class consists of cylinders with one end asymptotic to a Delaunay surface. The second class presents surfaces with a closed planar geodesic. In the third class each surface has a closed curve of points with a common tangent plane. An appendix, by the t...

Coplanar Constant Mean Curvature Surfaces

We consider constant mean curvature surfaces with finite topology, properly embedded in three-space in the sense of Alexandrov. Such surfaces with three ends and genus zero were constructed and completely classified by the authors [GKS2, GKS1]. Here we extend the arguments to the case of an arbitrary number of ends, under the assumption that the asymptotic axes of the ends lie in a common plane...

Surfaces of Constant Mean Curvature