Global existence and convergence of solutions of Calabi flow on surfaces of genus $h\geq 2$

Abstract

In this paper, based on a kind of Harnack estimate for the Calabi flow on surfaces, we show the longtime existence and convergence of solutions of 2-dimensional Calabi flow on surfaces $(\Sigma ,g_{0})$ of genus $h \geq 2$ with any arbitrary background metric $g_{0}$.