Geodesic
On the connectedness of the space of initial data for the Einstein equations
Smith, Brian1 ; Weinstein, Gilbert1
1 University of Alabama at Birmingham, Birmingham, AL 35205
Electronic research announcements of the American Mathematical Society, Tome 06 (2000), pp. 52-63 Cet article a éte moissonné depuis la source American Mathematical Society

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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 $\mathcal {M}$ 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 $\mathcal {M}$ is connected.
DOI : 10.1090/S1079-6762-00-00081-0

Smith, Brian 1 ; Weinstein, Gilbert 1

1 University of Alabama at Birmingham, Birmingham, AL 35205 
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Smith, Brian; Weinstein, Gilbert. On the connectedness of the space of initial data for the Einstein equations. Electronic research announcements of the American Mathematical Society, Tome 06 (2000), pp. 52-63. doi: 10.1090/S1079-6762-00-00081-0

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