In this paper we prove that given a smoothly conformally compact metric there
is a short-time solution to the Ricci flow that remains smoothly conformally
compact. We adapt recent results of Schn\"urer, Schulze and Simon to prove a
stability result for conformally compact Einstein metrics sufficiently close to
the hyperbolic metric.Comment: 26 pages, 2 figures. Version 2 includes stronger stability result and
fixes several typo