Conference Agenda

We study asymptotically Euclidean initial data sets for isolated gravitational systems and analyze the extrinsic curvature under geometric decay assumptions on the metric and mean curvature, together with standard matter decay. Using the York decomposition, we obtain a precise expansion and improved decay for the longitudinal part, while showing that the transverse-tracefree part is uncontrolled. Via the conformal method, this yields infinite-dimensional families with arbitrary asymptotic behaviour, no parity assumptions, and well-defined ADM angular momentum. The expansion also enables constructions with prescribed linear and angular momenta and quantifies their variation under perturbations, including perturbations of Kerrian data.