The Mean Curvature Type Flow in Lorentzian Warped Product

Power Mean Curvature Flow in Lorentzian Manifolds

We study the motion of an n-dimensional closed spacelike hypersurface in a Lorentzian manifold in the direction of its past directed normal vector, where the speed equals a positive power p of the mean curvature. We prove that for any p ∈ (0, 1], the flow exists for all time when the Ricci tensor of the ambient space is bounded from below on the set of timelike unit vectors. Moreover, if we ass...

Hypersurfaces with Constant Mean Curvature in a Lorentzian Space Form

The Scalar Curvature Flow in Lorentzian Manifolds

We prove the existence of closed hypersurfaces of prescribed scalar curvature in globally hyperbolic Lorentzian manifolds provided there are barriers.

Mean Curvature Blowup in Mean Curvature Flow

In this note we establish that finite-time singularities of the mean curvature flow of compact Riemannian submanifolds M t →֒ (N, h) are characterised by the blow up of the mean curvature.

hypersurfaces with constant mean curvature in a lorentzian space form