 
Summary: SCALAR CURVATURE, METRIC DEGENERATIONS AND THE STATIC
VACUUM EINSTEIN EQUATIONS ON 3MANIFOLDS, I.
MICHAEL T. ANDERSON
Contents
0. Introduction. 1
1. Background Material. 6
2. Initial Global Estimates for Yamabe Metrics. 17
3. Existence of NonFlat BlowUps. 26
4. Remarks on the Hypotheses. 53
5. Completeness of the Blowup Limits. 58
6. Construction of Yamabe Sequences with Singular Limits. 65
7. PalaisSmale Sequences for Scalar Curvature Functionals. 84
8. Appendix. 88
References 93
0. Introduction
In this paper, we prove that degenerations of sequences of Yamabe metrics on 3manifolds are
modeled or described by solutions to the static vacuum Einstein equations. One underlying moti
vation to understand such degenerations is the question of existence of constant curvature metrics
on 3manifolds, in other words with the geometrization conjecture of Thurston [Th2]. An approach
towards resolving this conjecture via study of Yamabe metrics is outlined in [An1].
