Asymptotically hyperbolic manifolds with polyhomogeneous metric

Details Asymptotically hyperbolic manifolds with polyhomogeneous metric Asymptotically hyperbolic manifolds with polyhomogeneous metric

2008-11-27

arxiv.org/abs/0811.4473v2

Mathematics

Analysis of PDEs

22 pages, mistake on previous version corrected

Scientific paper

We analyze the resolvent and define the scattering matrix for asymptotically
hyperbolic manifolds with metrics which have a polyhomogeneous expansion near
the boundary, and also 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.

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