On a conformal gap and finiteness theorem for a class of four manifolds

Details On a conformal gap and finiteness theorem for a class of four manifolds On a conformal gap and finiteness theorem for a class of four manifolds

2005-08-30

arxiv.org/abs/math/0508621v2

Mathematics

Differential Geometry

a new Section 6. 34 pages. to appear in GAFA

Scientific paper

In this paper we develop a bubble tree structure for a degenerating class of Riemannian metrics satisfying some global conformal bounds on compact manifolds of dimension 4. Applying the bubble tree structure, we establish a gap theorem, a finiteness theorem for diffeomorphism type for this class, and a diameter bound for a family of conformal metricssatisfying a suitable curvature equation.

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