Abstract
Suppose that M is a strictly pseudoconvex CR manifold bounding a compact complex manifold X of complex dimension m. Under appropriate geometric conditions on M, the manifold X admits an approximate Kähler–Einstein metric g which makes the interior of X a complete Riemannian manifold. We identify certain residues of the scattering operator on X as conformally covariant differential operators on M and obtain the CR Q-curvature of M from the scattering operator as well. In order to construct the Kähler–Einstein metric on X, we construct a global approximate solution of the complex Monge– Ampère equation on X, using Fefferman’s local construction for pseudoconvex domains in Cm. Our results for the scattering operator on a CR-manifold are the analogue in CR-geometry of Graham and Zworski’s result on the scattering operator on a real conformal manifold.
Original language | English |
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Pages (from-to) | 197-227 |
Number of pages | 31 |
Journal | Analysis and PDE |
Volume | 1 |
Issue number | 2 |
DOIs | |
State | Published - 2008 |
Bibliographical note
Publisher Copyright:© 2008, Analysis and PDE. All Rights Reserved.
Keywords
- Cr geometry
- Geometric scattering theory
- Q curvature
ASJC Scopus subject areas
- Analysis
- Numerical Analysis
- Applied Mathematics