In this talk I will present two recent results on the construction of initial data solving the constraint equations and which suits the decay requirements of either Minkowski stability or Kerr stability. The Minkowski result is the most technical since KIDS are handle by Kerr asymptotics, the control of which requires some work. The Kerr result benefits from the presence of the event horizon and the freedom in choosing the boundary condition for the conformal method. In particular, we are able to completely avoid the KIDS. This is joint work with Allen Juntao Fang and Jérémie Szeftel.
Arthur Touati (Paris): Initial data for stability theorems in general relativity
