Some conformally invariant gap theorems for Bach-flat 4-manifolds

2018/10/13 by Siyi Zhang, Zhang, Siyi · 1 citation
Mathematics · #53A30 #53C21 #Analysis of PDEs (math.AP) #Combinatorics #Conformal map #Differential Geometry (math.DG) #FOS: Mathematics #Fundamental theorem #Gap theorem #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #Geometry and complex manifolds #Invariant (physics) #Mathematical analysis #Mathematical physics #Mathematics #Pure mathematics #math.AP #math.DG #msc:53A30 #msc:53C21

paper · pdf · doi:10.48550/arxiv.1810.05897

published in arXiv (Cornell University) (Cornell University) · 11 pages

arxiv created 2018/10/13 · openalex publication_date 2018/10/13 · arxiv updated 2018/10/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/08

Abstract

Around 2007, A. Chang, J. Qing, and P. Yang proved a conformal gap theorem for Bach-flat metrics with round sphere as the model case. In this article, we extend this result to prove conformally invariant gap theorems for Bach-flat 4-manifolds with (\mathbbCP², g_FS) and (\mathbbS²×\mathbbS²,g_prod) as model cases. An iteration argument plays an important role in the case of (\mathbbCP², g_FS) and the convergence theory of Bach-flat metrics is of particular importance in the case of (\mathbbS²×\mathbbS²,g_prod).

Cited by

• Conformally invariant rigidity theorems on four-manifolds with boundary

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