Stronger Chern conjecture for minimal hypersurfaces

Let $M^n$ be a closed, minimally immersed hypersurface of the unit sphere $\mathbb{S}^{n+1}$ with constant scalar curvature. Stronger version of Chern's conjecture. Then $M^n$ is isoparametric. Motivated by isoparametric theory, this hypersurface formulation strengthens the general discreteness conjecture. Isoparametric hypersurfaces are the only known examples described in the source, and the conjecture remains open in general.