Аннотация:Standard methods in nonlinear analysis are used to indicate that there exists a parabolic branching of solutions of the Lichnerowicz–York equation with an unscaled source. We also apply these methods to the extended conformal thin sandwich formulation and, by assuming that the linearized system develops a kernel solution for sufficiently large initial data, we reproduce the parabolic solution curves for the conformal factor, lapse and shift found numerically by Pfeiffer and York.
