Eric Ling: Existence and nonexistence of CMC Cauchy surfaces in cosmological spacetimes

CMC (constant mean curvature) Cauchy surfaces play an important role in mathematical relativity. For example, finding solutions to the vacuum Einstein constraint equations is simplified by assuming CMC initial data. In this talk, we review and extend some results concerning the existence and nonexistence of CMC Cauchy surfaces in cosmological spacetimes, i.e., Lorentzian manifolds with compact Cauchy surfaces satisfying the strong energy condition (Ricci nonnegative on timelike vectors). Our results are also applicable to the case of a positive cosmological constant. This talk is based on joint work with Greg Galloway and with Argam Ohanya.