## Seminar on Geometric Complex Analysis

Date, time & place Monday 10:30 - 12:00 128Room #128 (Graduate School of Math. Sci. Bldg.) Kengo Hirachi, Shigeharu Takayama

### 2018/06/25

10:30-12:00   Room #128 (Graduate School of Math. Sci. Bldg.)
Stephen McKeown (Princeton University)
Cornered Asymptotically Hyperbolic Spaces
[ Abstract ]
This talk will concern cornered asymptotically hyperbolic spaces, which have a finite boundary in addition to the usual infinite boundary. I will first describe the construction a normal form near the corner for these spaces. Then I will discuss formal existence and uniqueness, near the corner, of asymptotically hyperbolic Einstein metrics, with a CMC-umbilic condition imposed on the finite boundary. This is analogous to the Fefferman-Graham construction for the ordinary, non-cornered setting. Finally, I will present work in progress regarding scattering on such spaces.