I'm studying by myself Mean Curvature Flow and I'm reading Lecture Notes on Mean Curvature Flow by Xi-Ping Zhu. The doubt of the title of this topic arised when I read the proof of the following result:
$\textbf{Corollary 2.7 (Preserving convexity)}$
Let $X(\cdot, t)$ be a solution of the mean curvature flow. Suppose the initial hypersurface $X(\cdot,0)$ is a convex and compact hypersurface, then $X(\cdot,t)$ is also a convex and compact hypersurface for $t > 0$.
$\textbf{Proof.}$ Applying the strong maximum principle, we know that $H(\cdot, t) > 0$ for $t > 0$. Combining Proposition $2.6$, we deduce that the second fundamental form of $X(\cdot, t)$ is positive definite for $t > 0$. To show $X(\cdot, t)$ remains embedded, we argue by contradiction. Suppose for some first time $t_0 > 0$ the solution $X(\cdot, t)$ develops a self-intersection. Clearly, at this self-intersection point, there must be a piece of hypersurface which has negative second fundamental form. This contradicts with the fact the second fundamental form of $X(\cdot, t)$ is positive definite everywhere for $t > 0$. $\square$
I didn't understand this part:
Clearly, at this self-intersection point, there must be a piece of hypersurface which has negative second fundamental form.
It seems to be a well-known result, but I didn't find this result. Can anyone indicate a reference for this result?
Thanks in advance!