Stability for small data: the drift model of the conformal method

Abstract: The conformal method in general relativity aims to successfully parametrise the set of all initial data associated with globally hyperbolic spacetimes. One such mapping was suggested by David Maxwell. I verify that the solutions of the corresponding conformal system are stable, in the sense that they present a priori bounds under perturbations of the system's coefficients. This result holds in dimensions $3\leq n\leq 5$, when the metric is conformally flat, the drift is small. A scalar field with suitably high potential is considered in this case.