A "boundedness implies convergence" principle and its applications to collapsing estimates in Kähler geometry. (May 2021)

• Record Type: Journal Article
• Authors: Jian, Wangjian; Shi, Yalong
• Is Part Of: Nonlinear analysis. Volume 206(2021)
• Publication Date: 2021-05
• Subjects: Mathematical analysis -- Periodicals; Functional analysis -- Periodicals; Nonlinear theories -- Periodicals; Analyse mathématique -- Périodiques; Analyse fonctionnelle -- Périodiques; Théories non linéaires -- Périodiques; Functional analysis; Mathematical analysis; Nonlinear theories; Periodicals; Electronic journals; 515.7248
• DOI: 10.1016/j.na.2021.112255
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: We establish a general "boundedness implies convergence" principle for a family of evolving Riemannian metrics. We then apply this principle to collapsing Calabi–Yau metrics and normalized Kähler–Ricci flows on minimal models to obtain convergence results.