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 Volume 8, Number 6, 2018, Pages 1919-1937 Estimate for evolutionary surfaces of prescribed mean curvature and the convergence Peihe Wang,Xinyu Gao Keywords:Mean curvature flow, gradient estimate, convergence. Abstract: In the paper, we will discuss the gradient estimate for the evolutionary surfaces of prescribed mean curvature with Neumann boundary value under the condition $f_\tau\ge -\kappa$, which is the same as the one in the interior estimate by K. Ecker and generalizes the condition $f_\tau\ge 0$ studied by Gerhardt etc. Also, based on the elliptic result obtained recently, we will show the longtime behavior of surfaces moving by the velocity being equal to the mean curvature. PDF      Download reader