Lawson–Simons conjecture for submanifolds in spheres

Let $F_{0}:M^{n}\to\mathbb{S}^{n+q}$ be an $n$-dimensional closed submanifold satisfying

$$|h|^{2}<2\sqrt{n-1},$$

where $h$ is the second fundamental form. Lawson–Simons conjecture. The mean curvature flow with initial value $F_{0}$ converges to a round point or a totally geodesic sphere. In particular, $M_{0}$ is diffeomorphic to $\mathbb{S}^{n}$. The source presents this as a special case motivated by the minimum of the pinching function and explicitly states that the Lawson–Simons conjecture remains open.