Breakdown criteria of Einstein equations in CMC gauge Seminar

I will report my work [1,2] on the geometric criterion for the breakdown of Einstein vacuum space-times with the constant mean curvature (CMC) foliation. In this work, the criterion is formulated in terms of time-integrability of the sup- norms of the second fundamental form and derivatives of the lapse function
associated to CMC foliation of the space-time. This result is obtained through deriving uniform lower bound on the null radius of injectivity of the light cones.

[1] Improved breakdown criterion for Einstein vacuum equation in CMC
gauge, Comm. Pure Appl. Math, Vol. LXV, 0021-0076 (2012)

[2] On Ricci coefficients of null hypersurfaces with time foliation in
Einstein vacuum space-time: Part I, accepted by Calculus of variations and
PDE (arXiv:1006.5963)