Canonical metrics on 3-manifolds and 4-manifolds

By Michael T. Anderson. 2005

61 citations recorded by the source corpus.

We prove certain weak or idealized existence results for minimizers of the natural quadratic curvature functionals on the space of metrics on 4-manifolds. Overall, we try to exhibit the relations with the picture in 3-dimensions provided by Thurston geometrization. The existence results apply in particular to the structure of the moduli spaces of such metrics, and as such generalize most of the known results for moduli of Einstein metrics.

Subfields: Applied Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/0fed3eb864e715b3bcbd47d75f8ae367162d291b

How researchers see this paper

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In Applied Mathematics

1. Bing Wang
2. Xiuxiong Chen
3. E. Humbert
4. J. Lott
5. Bruce Kleiner
6. Bernd Ammann
7. Mattias Dahl
8. Nicola Gigli

In Geometry and Topology

1. Bing Wang
2. Xiuxiong Chen
3. Mattias Dahl
4. J. Lott
5. Bruce Kleiner
6. E. Humbert
7. Bernd Ammann
8. Nicola Gigli

Citations in the corpus

• Notes on Perelman's papers (2006, methodology): “Our use of RminV (g) 2 3 and the sigma-invariant σ(M), instead of λ(g)V (g) 2 3 and λ, is inspired by [4].”
• Smooth Yamabe invariant and surgery (2008, background): “For example, LeBrun [36] showed that if a compact 4-dimensional manifold M carries a Kähler-Einstein metric with non-positive scalar curvature, then the supremum is attained by the conformal class of this metric.”
• Space of Ricci Flows I (2009, methodology): “The work of Anderson’s [ An05 ], [An06] also elaborated on this theme.”