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

Alice Chang; Jie Qing; Paul Yang

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

Differential Geometry 2007-05-23 v2 Analysis of PDEs

Authors: Alice Chang , Jie Qing , Paul Yang

Abstract

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.

Keywords

riemannian metrics conformal bounds bubble tree gap theorem finiteness theorem four manifolds

Cite

@article{arxiv.math/0508621,
  title  = {On a conformal gap and finiteness theorem for a class of four manifolds},
  author = {Alice Chang and Jie Qing and Paul Yang},
  journal= {arXiv preprint arXiv:math/0508621},
  year   = {2007}
}

Comments

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

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

Abstract

Keywords

Cite

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