Outdated Archival Version

These pages are not updated anymore. They reflect the state of 20 August 2005. For the current production of this journal, please refer to http://www.math.psu.edu/era/.

This journal is archived by the American Mathematical Society. The master copy is available at http://www.ams.org/era/

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

TeX source (42.9K)
DVI (63.5K)
PostScript (185.6K)

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