Static flow on complete noncompact manifolds I: short-time existence and   asymptotic expansions at conformal infinity
  In this paper, we study short-time existence of static flow on complete noncompact asymptotically static manifolds from the point of view that the stationary points of the evolution equations can be interpreted as static solutions of the Einstein vacuum equations with negative cosmological constant. For a static vacuum $(M^n,g,V),$ we also compute the asymptotic expansions of $g$ and $V$ at conformal infinity. 
Xue Hu, Yuguang Shi
math.DG