Convergence of Closed Pseudo-Hermitian Manifolds

2018/02/20 by Shu-Cheng Chang, Yuxin Dong, Chang, Shu-Cheng +3
Mathematics · Physics and Astronomy · #32V05 #53C25 #Advanced Differential Geometry Research #Convergence (economics) #Differential Geometry (math.DG) #Economics #FOS: Mathematics #Geology #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Hermitian matrix #Mathematical analysis #Mathematics #Pure mathematics #math.DG #msc:32V05 #msc:53C25

paper · pdf · doi:10.48550/arxiv.1802.07087

26 pages

arxiv created 2018/02/20 · openalex publication_date 2018/02/20 · arxiv updated 2018/02/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Based on uniform CR Sobolev inequality and Moser iteration, this paper investigates the convergence of closed pseudo-Hermitian manifolds. In terms of the subelliptic inequality, the set of closed normalized pseudo-Einstein manifolds with some uniform geometric conditions is compact. Moreover, the set of closed normalized Sasakian η-Einstein (2n+1)-manifolds with Carnot-Carathéodory distance bounded from above, volume bounded from below and L^{n + (1)/(2)} norm of pseudo-Hermitian curvature bounded is C^∞ compact. As an application, we will deduce some pointed convergence of complete Kähler cones with Sasakian manifolds as their links.

Citations

• Convergence and rigidity of manifolds under Ricci curvature bounds

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