CR-invariants and the scattering operator for complex manifolds with CR-boundary

Peter D. Hislop; Peter A. Perry; Siu Hung Tang

doi:10.1016/j.crma.2006.03.003

CR-invariants and the scattering operator for complex manifolds with CR-boundary

Mathematics

Producción científica: Article › revisión exhaustiva

2 Citas (Scopus)

Resumen

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).

Idioma original	English
Páginas (desde-hasta)	651-654
Número de páginas	4
Publicación	Comptes Rendus Mathematique
Volumen	342
N.º	9
DOI	https://doi.org/10.1016/j.crma.2006.03.003
Estado	Published - may 1 2006

Nota bibliográfica

Funding 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).

Financiación

We are grateful to Charles Epstein, Robin Graham, John Lee, and Ant\u00F4nio S\u00E1 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).

Financiadores	Número del financiador
U.S. Department of Energy Chinese Academy of Sciences Guangzhou Municipal Science and Technology Project Oak Ridge National Laboratory Extreme Science and Engineering Discovery Environment National Science Foundation National Energy Research Scientific Computing Center National Natural Science Foundation of China	DMS 04-08419, DMS 05-03784

ASJC Scopus subject areas

General Mathematics

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10.1016/j.crma.2006.03.003

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title = "CR-invariants and the scattering operator for complex manifolds with CR-boundary",

abstract = "Suppose that M is a CR manifold bounding a compact complex manifold X. The manifold X admits an approximate K{\"a}hler-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 Poincar{\'e}-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).",

author = "Hislop, \{Peter D.\} and Perry, \{Peter A.\} and Tang, \{Siu Hung\}",

note = "Funding Information: We are grateful to Charles Epstein, Robin Graham, John Lee, and Ant{\^o}nio S{\'a} 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).",

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AU - Hislop, Peter D.

AU - Perry, Peter A.

AU - Tang, Siu Hung

N1 - Funding 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).

PY - 2006/5/1

Y1 - 2006/5/1

N2 - 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).

AB - 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).

UR - https://www.scopus.com/pages/publications/33645989735

UR - https://www.scopus.com/pages/publications/33645989735#tab=citedBy

U2 - 10.1016/j.crma.2006.03.003

DO - 10.1016/j.crma.2006.03.003

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VL - 342

SP - 651

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JO - Comptes Rendus Mathematique

JF - Comptes Rendus Mathematique

IS - 9

ER -

CR-invariants and the scattering operator for complex manifolds with CR-boundary

Resumen

Nota bibliográfica

Financiación

ASJC Scopus subject areas

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