Geometric Analysis and Topology Seminar

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Null Mean Curvature Flow and Marginally Outer Trapped Surfaces

Speaker: Kristen Moore, Potsdam University and MSRI

Location: Warren Weaver Hall 512

Date: Wednesday, November 13, 2013, 11 a.m.

Synopsis:

In this talk we discuss a new second order parabolic evolution equation for hypersurfaces in space-time initial data sets, that generalises mean curvature flow (MCF). In particular, the 'null mean curvature' - a space-time extrinsic curvature quantity - replaces the usual mean curvature in the evolution equation defining MCF. This flow is motivated by the study of black holes and mass/energy inequalities in general relativity. We present a theory of weak solutions using level-set methods and an appropriate variational principle, and outline a natural application of the flow as a parabolic approach to constructing outermost marginally outer trapped surfaces (MOTS), which play the role of quasi-local black hole boundaries in general relativity. This is joint work with Theodora Bourni.