Q-curvature of Weyl structures and Poincar\'e metrics

We study an asymptotic Dirichlet problem for Weyl structures on asymptotically hyperbolic manifolds. By the bulk-boundary correspondence, or more precisely by the Fefferman-Graham theorem on Poincar\'e metrics, this leads to a natural extension of the notion of Branson's $Q$-curvature to Weyl structures on even-dimensional conformal manifolds.