  In this paper, the authors consider an initial boundary value problem for the
heat flow of equation of surfaces with constant mean curvatures, which was
investigated in [On the heat flow of equation of surfaces of constant mean
curvatures, Manuscripta Mathematica, 2011, 134: 259-271] by Huang et al., where
global well-posedness and finite time blow-up of regular solutions were
obtained. Their results are complemented in this paper in the sense that some
new conditions on the initial data are provided for the solutions to develop
finite time singularity.
