Suppose that M is a CR manifold bounding a compact complex manifold X. 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 as CR-covariant differential operators and obtain the CR Q-curvature of M from the scattering operator as well. Our results are an analogue in CR-geometry of Graham and Zworski's result that certain residues of the scattering operator on a conformally compact manifold with a Poincaré-Einstein metric are natural, conformally covariant differential operators, and the Q-curvature of the conformal infinity can be recovered from the scattering operator. To cite this article: P.D. Hislop et al., C. R. Acad. Sci. Paris, Ser. I 342 (2006).
|Number of pages||4|
|Journal||Comptes Rendus Mathematique|
|State||Published - May 1 2006|
Bibliographical noteFunding Information:
We are grateful to Charles Epstein, Robin Graham, John Lee, and Antônio Sá Barretto for helpful discussions and correspondence. P.A.P. thanks the National Center for Theoretical Science at the National Tsing Hua University, Hsinchu, Taiwan, for hospitality during part of the time that this work was done. The authors are partially supported by NSF grants DMS 05-03784 (Hislop) and DMS 04-08419 (Perry).
ASJC Scopus subject areas
- Mathematics (all)