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On the connectedness of the space of initial data for the Einstein equations
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On the connectedness of the space of initial data for the Einstein equations
Brian Smith and Gilbert Weinstein
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.
Copyright 2000 American Mathematical Society
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Article Info
- ERA Amer. Math. Soc. 06 (2000), pp. 52-63
- Publisher Identifier: S 1079-6762(00)00081-0
- 2000 Mathematics Subject Classification. Primary 83C05; Secondary 58G11
- Received by the editors May 27, 1999
- Posted on July 19, 2000
- Communicated by Richard Schoen
- Comments (When Available)
Brian Smith
University of Alabama at Birmingham, Birmingham, AL 35205
E-mail address: smith@math.uab.edu
Gilbert Weinstein
University of Alabama at Birmingham, Birmingham, AL 35205
E-mail address: weinstei@math.uab.edu
This research was supported in part by NSF grant DMS~9704760
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