Canonical metrics on 3-manifolds and 4-manifolds

Details Canonical metrics on 3-manifolds and 4-manifolds Canonical metrics on 3-manifolds and 4-manifolds

2005-11-02

arxiv.org/abs/math/0511034v1

Mathematics

Differential Geometry

32 pages, article In Memory of S.S. Chern

Scientific paper

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.

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