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

Chang, Alice; Qing, Jie; Yang, Paul

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

Authors

Chang, Alice

Qing, Jie

Yang, Paul

Description

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