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

Alice Chang; Jie Qing; Paul Yang

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

Alice Chang·Jie Qing·Paul Yang

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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.

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Alice Chang, Jie Qing, Paul Yang. 2006-08-29. On a conformal gap and finiteness theorem for a class of four manifolds. https://arxiv.org/abs/math/0508621

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