Singularities of null mean curvature flow of null hypersurfaces in Lorentzian manifolds

Abstract

We classify two main singularities, as type I and type II, associated with null mean curvature flow of screen conformal null hypersurfaces in Lorentzian manifolds. We prove that the flow at a type I singularity is asymptotically self-similar, whereas at a type II singularity there is a blow-up solution which is an eternal solution. For further analysis of the above two singularities, we define null translating solitons and use them to prove some Harnack estimates for null mean curvature flow under certain geometric conditions.