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.

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 I singularity otherwise.

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

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.