Large Time Behavior of Radially Symmetric Surfaces in the Mean Curvature Flow

@article{Nara2008LargeTB,
  title={Large Time Behavior of Radially Symmetric Surfaces in the Mean Curvature Flow},
  author={Mitsunori Nara},
  journal={SIAM J. Math. Analysis},
  year={2008},
  volume={39},
  pages={1978-1995}
}
The large time behavior of radially symmetric surfaces in $\mathbb{R}^{n+1}$ moving by the mean curvature flow is studied. By studying a Cauchy problem, we deal with moving surfaces represented by entire graphs on a hyperplane. Here an initial surface is given by a function that is bounded and radially symmetric. It is proved that the solution converges uniformly to the solution of the Cauchy problem of the heat equation with the same initial value. The difference is of order $O(t^{-1/2})$ as… CONTINUE READING

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