Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
|
   
Available in electronic format
Available in print format
Transactions of the American Mathematical Society
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
MathSciNet review: 2465828
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 $ 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)


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.




AMS and Social Media LinkedIn Facebook Podcasts Twitter YouTube RSS Feeds Blogs Wikipedia