Finite time blow-up for the heat flow of $H$-surface with constant mean curvature

We consider an initial boundary value problem for the heat flow of the equation of surfaces with constant mean curvature which was investigated in [T. Huang et al., Manuscripta Math. 134 (2011)], 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.