We analyze the resolvent and define the scattering matrix for asymptotically hyperbolic manifolds with metrics which have a polyhomogeneous expansion near the boundary. We prove that there is always an essential singularity of the resolvent in this setting. We use this analysis to prove an inverse result for conformally compact odd-dimensional Einstein manifolds.
"Asymptotically hyperbolic manifolds with polyhomogeneous metric." Differential Integral Equations 24 (9/10) 973 - 1000, September/October 2011. https://doi.org/10.57262/die/1356012896