Geometry Seminar: M. Wolff (KTH)
Geometry Seminar (Geometric Analysis)
Speaker: Markus Wolff (KTH)
Title: Foliations of asymptotically Schwarzschildean lightcones by surfaces of constant spacetime mean curvature
Speaker: Markus Wolff (KTH)
Title: Foliations of asymptotically Schwarzschildean lightcones by surfaces of constant spacetime mean curvature
Abstract: We construct asymptotic foliations of asymtotically Schwarzschildean lightcones by surfaces of constant spacetime mean curvature (STCMC). For a surface in an ambient spacetime, the spacetime mean curvature is defined as the (Lorentzian) length of the co-dimension 2 mean curvature vector. Asymptotic foliations of asymptotically flat spacelike hypersurfaces by STCMC surfaces have previously been constructed by Cederbaum-Sakovich to define a geometric notion of center of mass.
Our construction is motivated by the approach of Huisken-Yau in employing a geometric flow. We show that any initial surface within a sufficient a-priori class converges exponentially to an STCMC surface under area preserving null mean curvature flow. We further show that the resulting STCMC surfaces form an asymptotic foliation that is unique within the given a-priori class. This is joint work with Klaus Kröncke.