# 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} }

- Published in SIAM J. Math. Analysis 2008
DOI:10.1137/070686330

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

#### Topics from this paper.

#### Citations

##### Publications citing this paper.

SHOWING 1-3 OF 3 CITATIONS

## Mean curvature flow of entire graphs evolving away from the heat flow

VIEW 6 EXCERPTS

CITES BACKGROUND

HIGHLY INFLUENCED

## a new class of fully nonlinear curvature flows

VIEW 1 EXCERPT

CITES BACKGROUND