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

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