CR-Invariants and the Scattering Operator for Complex Manifolds with Boundary

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dc.creatorHislop, Peter D.
dc.creatorPerry, Peter A.
dc.creatorTang, Siu-Hung
dc.date2007-09-07
dc.date.accessioned2026-07-07T08:28:12Z
dc.date.available2026-07-07T08:28:12Z
dc.descriptionThe purpose of this paper is to describe certain CR-covariant differential operators on a strictly pseudoconvex CR manifold $M$ as residues of the scattering operator for the Laplacian on an ambient complex Kähler manifold $X$ having $M$ as a `CR-infinity.' We also characterize the CR $Q$-curvature in terms of the scattering operator. Our results parallel earlier results of Graham and Zworski \cite{GZ:2003}, who showed that if $X$ is an asymptotically hyperbolic manifold carrying a Poincaré-Einstein metric, the $Q$-curvature and certain conformally covariant differential operators on the `conformal infinity' $M$ of $X$ can be recovered from the scattering operator on $X$. The results in this paper were announced in \cite{HPT:2006}.
dc.description32 pages
dc.identifierhttps://arxiv.org/abs/0709.1103
dc.identifierhttp://arxiv.org/abs/0709.1103
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/137534
dc.subjectAnalysis of PDEs
dc.subjectComplex Variables
dc.subject58J05, 58J50, 32V05, 32V20
dc.titleCR-Invariants and the Scattering Operator for Complex Manifolds with Boundary
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