"Null mean curvature" flow and marginally outer trapped surfaces

16 May 2016
In this talk we discuss a new second order parabolic evolution equation
for hypersurfaces in space-time initial data sets, that generalizes 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 the level-set
method and  outline a natural application of the flow as a parabolic
approach to finding outermost marginally outer trapped surfaces (MOTS),
which play the role of quasi-local black hole boundaries in general
relativity. This is joint work with Kristen Moore.
  • Partial Differential Equations Seminar