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Summary: SCALAR CURVATURE, METRIC DEGENERATIONS, AND THE STATIC
VACUUM EINSTEIN EQUATIONS ON 3-MANIFOLDS, II.
MICHAEL T. ANDERSON
Contents
0. Introduction. 1
1. Remarks on the Choice of the Curvature Functional. 6
2. Brief Background. 11
3. Basic Properties of the Curvature Functional. 14
4. Blow-up Limits of the Minimizers. 28
5. Some Non-Existence Results. 42
6. Models for the Degeneration of the Minimizers. 44
7. Results on the Asymptotics of the Limits. 50
Appendix A. 68
Appendix B. 70
Appendix C. 71
References 75
0. Introduction.
Consider the problem of nding a constant curvature metric on a given closed 3-manifold M . It is
known that essential spheres and tori, (except in the case of
at manifolds), prevent the existence of
such metrics, but it is unknown if there are other topological obstructions. We approach this issue
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