A geometric choice of asymptotically Euclidean coordinates via STCMC-foliations

Asymptotically Euclidean initial data sets (IDS) in General Relativity model instants in time for isolated systems. In this talk, we show that an IDS is asymptotically Euclidean if it admits a cover by closed hypersurfaces of constant spacetime mean curvature (STCMC), provided these hypersurfaces satisfy certain geometric estimates, some weak foliation properties, and each