  In this paper, we use the modified potential well method to study the long
time behaviors of solutions to the heat flow of H-system in a bounded smooth
domain of $R^2$. Global existence and finite time blowup of solutions are
proved when the initial energy is in three cases. When the initial energy is
low or critical, we not only give a threshold result for the global existence
and blowup of solutions, but also obtain the decay rate of the $L^2$ norm for
global solutions. When the initial energy is high, sufficient conditions for
the global existence and blowup of solutions are also provided. We extend the
recent results which were obtained in [12].
