Abstract
AbstractThe goal of these notes is to make accessible to interested readers a case study where two prominent avenues of research of geometric analysis, Ricci flow and Einstein constraints theory, interact in a quite remarkable way. In particular, the theme we discuss and illustrate here is the characterization of a geometric averaging technique, induced by the Ricci flow, that allows us to compare a given (generalized) Einstein initial data set with another distinct Einstein initial data set, both supported on a given closed n-dimensional manifold, i.e., on a compact n-dimensional manifold \(\varSigma \) without boundary.
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