Evolving hypersurfaces by their inverse null mean curvature

Abstract

We introduce a new geometric evolution equation for hypersurfaces in asymptotically flat spacetime initial data sets, that unites the theory of marginally outer trapped surfaces (MOTS) with the study of inverse mean curvature flow in asymptotically flat Riemannian manifolds. A theory of weak solutions is developed using level-set methods and an appropriate variational principle. This new flow has a natural application as a variational-type approach to constructing MOTS, and this work also gives new insights into the theory of weak solutions of inverse mean curvature flow.

Cited by in corpus (5)

• On the Minkowski-type inequality for outward minimizing hypersurfaces in Schwarzschild space
• Time flat surfaces and the monotonicity of the spacetime Hawking mass
• Spacetime Harmonic Functions and Applications to Mass
• Mean curvature flow in null hypersurfaces and the detection of MOTS
• Null mean curvature flow and outermost MOTS