Constant mean curvature foliation: singularity structure and curvature estimate

Nonlinear quantum gravity on the constant mean curvature foliation

A new approach to quantum gravity is presented based on a nonlinear quantization scheme for canonical field theories with an implicitly defined Hamiltonian. The constant mean curvature foliation is employed to eliminate the momentum constraints in canonical general relativity. It is, however, argued that the Hamiltonian constraint may be advantageously retained in the reduced classical system t...

Singularity Structure in Mean Curvature Flow of Mean Convex Sets

In this note we announce results on the mean curvature flow of mean convex sets in 3-dimensions. Loosely speaking, our results justify the naive picture of mean curvature flow where the only singularities are neck pinches, and components which collapse to asymptotically round spheres. In this note we announce results on the mean curvature flow of mean convex sets; all the statements below have ...

Hypersurfaces with Constant Mean Curvature in a Lorentzian Space Form

A height estimate for constant mean curvature graphs and uniqueness

In this paper, we give a height estimate for constant mean curvature graphs. Using this result we prove two results of uniqueness for the Dirichlet problem associated to the constant mean curvature equation on unbounded domains. 2000 Mathematics Subject Classification. 53A10. Introduction The surfaces with constant mean curvature are the mathematical modelling of soap films. These surfaces appe...

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...