Evolving hypersurfaces by their inverse null mean curvature

TL;DR

This paper introduces a novel geometric evolution equation for hypersurfaces in spacetime, combining MOTS theory with inverse mean curvature flow, and develops a weak solution framework using level-set methods.

Contribution

It presents a new evolution equation uniting MOTS and inverse mean curvature flow, with a developed weak solution theory and applications to constructing MOTS.

Findings

Established a new geometric flow uniting MOTS and inverse mean curvature flow.

Developed a weak solution theory using level-set methods.

Provided insights into inverse mean curvature flow in asymptotically flat spacetimes.

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.