Eric Bahuaud, Seattle University
Title: Geometrically Finite Asymptotically Hyperbolic Einstein metrics
Abstract: Asymptotically hyperbolic Einstein metrics are
important in conformal geometry
and the physics of the AdS-CFT
correspondence. In 1991, Graham and Lee proved that any
sufficiently
small perturbation (in Holder norm) of the round metric on the unit
sphere (with
dimension at least 3) is the "conformal infinity" of an
asymptotically hyperbolic Einstein
metric on the open unit ball. In
this talk I will give the background and explain the proof of
this
result, and then discuss recent joint work with Rochon proving the
existence of Einstein
metrics near certain geometrically finite
quotients of the hyperbolic metric.