Global existence and convergence of solutions of the Calabi flow on Einstein 4-manifolds

Abstract

In this paper, firstly, we show the Bondi-mass type estimate of solutions of Calabi flow on closed $4$-manifolds. Secondly, in our applications, we obtain the long time existence on closed $4$-manifolds. In particular, we are able to show the asymptotic convergence of a subsequence of solutions of the Calabi flow on closed Einstein $4$-manifolds.