Question: Suppose $N$ is an $n$ dimensional immersed submanifold in a complete, non-compact manifold $Ｍ$， with bounded geometry. Suppose the mean curvature flow $F:Ｎ\times [0,q)\rightarrow M$ satisfies $$\begin{split} \frac{d}{dt}F&=\vec{H};\ F(p,0)&=F_{0}; \end{split}$$ If $F(p,t)$ exists for $t\in [0,q)$, is there any possible the closure of $F(N\times[0,t))$ is unbounded in $M$. In other words, can the mean curvature flow go to infinity for a finite time? I didn't find the contra_example. I hope the answer is yes. In Euclidean space, definitely this is ture? Is any one know any related reference about this question? You are very appreciated if you can offer some opinions or information.
Question: Suppose $N$ is an $n$ dimensional immersed submanifold in a complete, non-compact manifold $Ｍ$， with bounded geometry. Suppose the mean curvature flow $F:Ｎ\times [0,q)\rightarrow M$ satisfies $$\begin{split} \frac{d}{dt}F&=\vec{H};\ F(p,0)&=F_{0}; \end{split}$$ If $F(p,t)$ exists for $t\in [0,q)$, is there any possible the closure of $F(N\times[0,t))$ is unbounded in $M$. In other words, can the mean curvature flow go to infinity for a finite time? I didn't find the contra_example. I hope the answer is yes. In Euclidean space, definitely this is ture? Is any one know any related reference about this question? You are very appreciated if you can offer some opinions or information.