Improved breakdown criterion for Einstein vacuum equations in CMC gauge

Qian Wang

Let $\M_*=\cup_{t\in [t_0, t_*)} Σ_t$ be a part of vacuum globally hyperbolic space-time $(\bM, \bg)$, foliated by constant mean curvature hypersurfaces ${\Sigma }_t$ with $t_0<t_{\ast }<0$. We…