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Electronic Research Announcements
Electronic Research Announcements
ISSN 1079-6762

On the connectedness of the space of initial data for the Einstein equations


Authors: Brian Smith and Gilbert Weinstein
Journal: Electron. Res. Announc. Amer. Math. Soc. 6 (2000), 52-63
MSC (2000): Primary 83C05; Secondary 58G11
Published electronically: July 19, 2000
MathSciNet review: 1777856
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Abstract:

Is the space of initial data for the Einstein vacuum equations connected? As a partial answer to this question, we prove the following result: Let ${\EuScript M}$ be the space of asymptotically flat metrics of non-negative scalar curvature on ${\mathbb R}^3$ which admit a global foliation outside a point by $2$-spheres of positive mean and Gauss curvatures. Then ${\EuScript M}$ is connected.


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Additional Information

Brian Smith
Affiliation: University of Alabama at Birmingham, Birmingham, AL 35205
Email: smith@math.uab.edu

Gilbert Weinstein
Affiliation: University of Alabama at Birmingham, Birmingham, AL 35205
Email: weinstei@math.uab.edu

DOI: http://dx.doi.org/10.1090/S1079-6762-00-00081-0
PII: S 1079-6762(00)00081-0
Received by editor(s): May 27, 1999
Published electronically: July 19, 2000
Additional Notes: This research was supported in part by NSF grant DMS 9704760.
Communicated by: Richard Schoen
Article copyright: © Copyright 2000 American Mathematical Society