| Résume | Asymptotically Euclidean 3-dimensional initial data sets were shown to
carry asymptotic foliations of closed hypersurfaces with constant
spacetime mean curvature (Cederbaum-Sakovich, 2021).
In order to prove the inverse implication of this result and hence the
geometric characterization of being asymptotically Euclidean, we start
from the purely geometric foliation and construct asymptotic
coordinates from it, exploiting the properties of the induced
Laplacian of the foliation leaves via a delicate analysis.
We show that these coordinates are asymptotically Euclidean, and
moreover seem well-adapted to the center of mass.
This is joint work with A. Piubello. |
