Let $M \times [0, T) \to \mathbb{R}^{n+1}$ be a mean curvature flow and let $T$ be a singular time. Let $A$ denote the second fundamental form.


We have a **type I singularity** if 
$$
\max\_{p \in M} |A(p, t)| \le \frac{C}{\sqrt{2(T-t)}}
$$
for some constant $C > 0$ and a **type II singularity** otherwise. 


Why are **type I singularities** of the mean curvature flow often called "fast forming singularities" and **type II singularities** "slow forming"? 
I don't understand the reason behind this terminology, since the second fundamental form is blowing up slower at type I singularities.



Slow and fast forming singularities of the mean curvature flow
I could be wrong but I believe the answer is disappointingly uninteresting: Set $f(t)\doteqdot \sup\_{M\times[0,t]}\vert A\vert^2$. If the flow is of type I then the remaining time is bounded by $1/f(t)$, so a 'singularity' occurs sooner than if the flow is not of type I.


