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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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