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SCALAR CURVATURE AND THE EXISTENCE OF GEOMETRIC STRUCTURES ON 3-MANIFOLDS, II
 

Summary: SCALAR CURVATURE AND THE EXISTENCE OF GEOMETRIC
STRUCTURES ON 3-MANIFOLDS, II
MICHAEL T. ANDERSON
Contents
0. Introduction. 1
1. Background Setting and Results. 3
2. The Linearized Equations. 10
3. Level Set Measures and Masses. 22
4. Uniformity Estimates. 27
5. Mass Gaps and Essential Spheres. 36
6. The Collapse Situation. 47
7. Non-Degeneration Situations. 51
Appendix A. 57
Appendix B. 58
References 60
Abstract. This paper studies the degeneration, i.e curvature blow-up, of sequences of metrics
approaching the Sigma constant (M) on 3-manifolds M with (M)  0. The degeneration is
related to the sphere decomposition of M in case M is -tame.
0. Introduction.
This paper is a continuation of [1], and is mainly concerned with the Sphere conjecture of [1,x0].

  

Source: Anderson, Michael - Department of Mathematics, SUNY at Stony Brook

 

Collections: Mathematics