Global stability of Minkowski spacetime with minimal decay

Understand

The global stability of Minkowski spacetime, a milestone in the field, has been proven in the celebrated work of Christodoulou and Klainerman \cite{Ch-Kl} in 1993.

• In 2007, Bieri \cite{Bieri} has extended the result of \cite{Ch-Kl} under lower decay and regularity assumptions on the initial data.
• In this paper, we extend the result of \cite{Bieri} to minimal decay assumptions.
• Also, concerning the treatment of curvature estimates, we replace the vectorfield method used in \cite{Ch-Kl,Bieri} by the $r^p$--weighted estimates of Dafermos and Rodnianski \cite{Da-Ro}.