2021/09/01 by Nikita Klemyatin, Klemyatin, Nikita
Mathematics · #Algebraic Geometry and Number Theory #Analysis of PDEs (math.AP) #Complex Variables (math.CV) #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds
paper · pdf · doi:10.48550/arxiv.2109.00312
openalex publication_date 2021/09/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The Type IIB flow is a flow of conformally balanced complex manifolds introduced by Phong, Picard, and Zhang, about whose singularities little is as yet known. We formulate convergence criteria for the Gromov-Cheeger-Hamilton convergence of sequences of Hermitian manifolds, and apply them to precompactness theorems and the existence of singularity models for the Type IIB flow, in analogy with Hamilton's classic compactness theorems and classification of singularities for the Ricci flow.