Ricci-flow-conjugated initial data sets for Einstein equations
Ricci-flow-conjugated initial data sets for Einstein equations
We discuss a natural form of Ricci-flow conjugation between two distinct general relativistic data sets given on a compact $n \ge 3$-dimensional manifold $\Sigma$. We establish the existence of the relevant entropy functionals for the matter and geometrical variables, their monotonicity properties, and the associated convergence in the appropriate sense. …