A Mean Curvature Type Flow in Space Forms

Hypersurfaces with Constant Mean Curvature in a Lorentzian Space Form

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

Lagrangian Mean Curvature Flow in Pseudo-euclidean Space

We establish the longtime existence and convergence results of the mean curvature flow of entire Lagrangian graphs in pseudo-Euclidean space.

Mean curvature flow

Mean curvature flow is the negative gradient flow of volume, so any hypersurface flows through hypersurfaces in the direction of steepest descent for volume and eventually becomes extinct in finite time. Before it becomes extinct, topological changes can occur as it goes through singularities. If the hypersurface is in general or generic position, then we explain what singularities can occur un...