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Transactions of the American Mathematical Society
ISSN 1088-6850(e) ISSN 0002-9947(p)
     

Wormholes in ACH Einstein manifolds

Author(s): Olivier Biquard; Yann Rollin
Journal: Trans. Amer. Math. Soc. 361 (2009), 2021-2046.
MSC (2000): Primary 32Q20, 53C25
Posted: November 25, 2008
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Abstract: We give a new construction of Einstein manifolds which are asymptotically complex hyperbolic, inspired by the work of Mazzeo-Pacard in the real hyperbolic case. The idea is to develop a gluing theorem for $ 1$-handle surgery at infinity, which generalizes the Klein construction for the complex hyperbolic metric.


References:

1.
A. L. Besse.
Einstein manifolds, volume 10 of Ergebnisse der Mathematik und ihrer Grenzgebiete (3) [Results in Mathematics and Related Areas (3)].
Springer-Verlag, Berlin, 1987. MR 867684 (88f:53087)

2.
O. Biquard.
Métriques d'Einstein asymptotiquement symétriques.
Astérisque, (265):vi+109, 2000. MR 1760319 (2001k:53079)

3.
O. Biquard and M. Herzlich.
A Burns-Epstein invariant for ACHE 4-manifolds.
Duke Math. J., 126(1):53-100, 2005. MR 2110628 (2006g:32034)

4.
J.-P. Bourguignon and H. B. Lawson, Jr.
Stability and isolation phenomena for Yang-Mills fields.
Comm. Math. Phys., 79(2):189-230, 1981. MR 612248 (82g:58026)

5.
D. M. J. Calderbank and M. A. Singer.
Einstein metrics and complex singularities.
Invent. Math., 156(2):405-443, 2004. MR 2052611 (2005h:53064)

6.
S. Y. Cheng and S. T. Yau.
On the existence of a complete Kähler metric on noncompact complex manifolds and the regularity of Fefferman's equation.
Comm. Pure Appl. Math., 33(4):507-544, 1980. MR 575736 (82f:53074)

7.
S. S. Chern and J. K. Moser.
Real hypersurfaces in complex manifolds.
Acta Math., 133:219-271, 1974. MR 0425155 (54:13112)

8.
X. Dai, X. Wang, and G. Wei.
On the stability of Kähler-Einstein metrics.
math.DG/0504527.

9.
Y. Eliashberg.
Topological characterization of Stein manifolds of dimension $ >2$.
Internat. J. Math., 1(1):29-46, 1990. MR 1044658 (91k:32012)

10.
C. L. Fefferman.
Monge-Ampère equations, the Bergman kernel, and geometry of pseudoconvex domains.
Ann. of Math. (2), 103(2):395-416, 1976. MR 0407320 (53:11097a)

11.
W. M. Goldman.
Complex hyperbolic geometry.
Oxford Mathematical Monographs. The Clarendon Press, Oxford University Press, New York, 1999.
Oxford Science Publications. MR 1695450 (2000g:32029)

12.
R. Mazzeo and F. Pacard.
Maskit combinations of Poincaré-Einstein metrics.
Adv. Math., 204(2):379-412, 2006. MR 2249618 (2007e:53052)

13.
N. Mok and S.-T. Yau.
Completeness of the Kähler-Einstein metric on bounded domains and the characterization of domains of holomorphy by curvature conditions.
In The mathematical heritage of Henri Poincaré, Part 1 (Bloomington, Ind., 1980), volume 39 of Proc. Sympos. Pure Math., pages 41-59. Amer. Math. Soc., Providence, RI, 1983. MR 720056 (85j:53068)

14.
A. Weinstein.
Contact surgery and symplectic handlebodies.
Hokkaido Math. J., 20(2):241-251, 1991. MR 1114405 (92g:53028)


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Additional Information:

Olivier Biquard
Affiliation: Institut de Recherche Mathématique Avancé, UMR 7501 du CNRS, Strasbourg, France
Email: Olivier.Biquard@math.u-strasbg.fr

Yann Rollin
Affiliation: Department of Mathematics, Imperial College, London, United Kingdom
Email: rollin@imperial.ac.uk

DOI: 10.1090/S0002-9947-08-04778-8
PII: S 0002-9947(08)04778-8
Received by editor(s): May 9, 2007
Posted: November 25, 2008
Additional Notes: The second author was partly supported by a University Research Fellowship of the Royal Society and NSF grant \#DMS-0305130
Copyright of article: Copyright 2008, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.


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