EINSTEIN EQUATIONS AND CONFORMAL STRUCTURE - EXISTENCE OF ANTI DE SITTER TYPE SPACE-TIMES

We discuss Einstein's equations in the context of normal conformal Cartan connections, derive a new conformal representation of the equations, and express the equations in a conformally invariant gauge. The resulting formulation of the equations is used to show the existence of asymptotically simple solutions to Einstein's equations with a positive cosmological constant. The solutions are characterized by Cauchy data on a space-like slice and by the intrinsic conformal structure on the conformal boundary at space-like and null infinity.