This talk will concern cornered asymptotically hyperbolic spaces, which
have a finite boundary in addition to the usual infinite boundary. After
introducing the setting, we will present a normal form near the corner for
these spaces. Using this, we will then discuss formal existence and
uniqueness, near the corner, of asymptotically hyperbolic Einstein metrics,
with a CMC-umbilic condition imposed on the finite boundary. We will
identify a new conformal hypersurface invariant and discuss applications to
conformal analysis of manifolds with boundary.
This is doctoral work under the supervision of C. Robin Graham.