| 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. |
| 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. |
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