|
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
Retrieve article in:
PDF
Abstract |
References |
Similar articles |
Additional information
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 -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 . 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)
Similar Articles:
Retrieve articles in Transactions of the American Mathematical Society
with MSC
(2000):
32Q20, 53C25
Retrieve articles in all Journals with MSC
(2000):
32Q20, 53C25
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.
|