The conformal method gives a poor parameterization of initial data

Because of the well-posedness of the Field Equations, one can parameterize the set of all spacetimes by parameterizing the set of all ”initial data” solving the Einstein constraint equations. The standard technique used in this attempt is the conformal method. This method performs admirably for initial data with constant and near-constant mean curvatures. However, more recent results have shown problems for far-from-constant mean curvature data. Notably, last year, The-Cang Nguyen found families of data on Yamabe positive manifolds which exhibit both non-existence and non-uniqueness in that regime, though this result was for a fairly special class of data. Recent (mostly numerical) work with Michael Holst and David Maxwell have shown that these results are much more general, though not universal. In this talk we will discuss these results, their implications, and possible future directions.Non UBCUnreviewedAuthor affiliation: UC: San DiegoPostdoctora