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Volume 8, Number 6, 2018, Pages 1919-1937                                                                DOI:10.11948/2018.1919
Estimate for evolutionary surfaces of prescribed mean curvature and the convergence
Peihe Wang,Xinyu Gao
Keywords:Mean curvature flow, gradient estimate, convergence.
      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.
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