Compactness theorems and the Calabi flow on Kähler surfaces with stable tangent bundle
Journal
Mathematische Annalen
Journal Volume
318
Journal Issue
2
Pages
315-340
Date Issued
2000
Author(s)
Abstract
In this paper, we prove some compactness theorems and collapse phenomenon on compact Kähler surfaces with stable tangent bundle. We then apply the results to the Calabi flow. More precisely, we prove, under suitable curvature conditions, the longtime existence and asymptotic convergence for solutions of the Calabi flow on compact Kahler surfaces admitting no nonzero holomorphic tangent vector fields and with stable tangent bundle. We also give some examples where the Calabi flow blows up.
Type
journal article