Why small $C^2$-perturbation of the sphere is a convex hypersurface? In fact, I don't know what is $C^2$-perturbation. Whether it mean the position vector $F(x,t)$ is $C^2$ about $t$? But in my view, this is not enough to show the small $C^2$-perturbation of the sphere is a convex hypersurface.
This question is origin from first line of 3th page of Blow-up of the mean curvature at the first singular time of the mean curvature flow.
Thanks for any help.