I am trying to develop some intuition into the properties of mean curvature flow of a surface in $\mathbb{R}^3$. As an example, I am trying to understand what happens to a surface of revolution $S = (f(u), g(u)\text{cos }v, g(u)\text{sin }v)$, $u \in [0, 1]$, $v \in [0, 2\pi]$. For example, what happens if $S$ is positively curved at all interior points? Or if $S$ is negatively curved at all interior points? Will it remain embedded for short time? Long time? How will it look in long time? I am trying to get some heuristic ideas. Thanks!
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