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

2005/08/30 by Alice Chang, Chang, Alice, Jie Qing +3
Mathematics · #35J60 #53C21 #Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #Geometry and complex manifolds #math.AP #math.DG #msc:35J60 #msc:53C21

paper · pdf · doi:10.48550/arxiv.math/0508621

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

openalex publication_date 2005/08/30 · arxiv created 2006/08/29 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Related

• Some Progress in Conformal Geometry
• Conformal metric sequences with integral-bounded scalar curvature
• Some conformally invariant gap theorems for Bach-flat 4-manifolds
• On the problem of filling by a Poincaré-Einstein metric in dimension 4
• On compactness conformally compact Einstein manifolds and uniqueness of Graham-Lee metrics, III