Evolution of a surface in 3-space

Question

Let $(M^3,g)$ be a $3$ dimensional simply connected compact riemannian variety and $\Sigma^2 \hookrightarrow M^3$ an immerged surface in $M^3$. I describe an evolution of $\Sigma^2$:

$$ \dot{x}(t)= N_{\Sigma^2(t)} (x(t))$$

where $N_{\Sigma^2}$ is the normal vector of $\Sigma^2$ in $M^3$. Does the surface converge towards points?