Geometry Seminar: E. Ling (Rutgers)

Geometry Seminar (Geometric Analysis)

Speaker: Eric Ling (Rutgers)

Title: On the existence of CMC Cauchy surfaces in cosmological spacetimes

Abstract: As is well known, constant mean curvature (CMC) spacelike hypersurfaces play an important role in solving the Einstein equations. However, a classical example of Bartnik along with vacuum examples by Chrusciel, Isenberg, and Pollack demonstrate that not all cosmological spacetimes (i.e. spacetimes with compact Cauchy surfaces) admit a CMC Cauchy surface. In this talk, I will show a recent CMC existence result established via a spacetime curvature condition along with some other CMC existence results motivated by a conjecture of Dilts and Holst. This is joint work with Gregory Galloway.