Closed Willmore minimal hypersurfaces with constant scalar curvature in S5(1) are isoparametric

In this paper, we will prove that any closed minimal Willmore hypersurface M4 of S5 with constant scalar curvature must be isoparametric. To be precise, M4 is either an equatorial 4 sphere, a product of sphere S2(22)×S2(22) or a Cartan's minimal hypersurface. In particular, the value of the second fundamental form S can only be 0, 4, 12. This result strongly supports Chern's Conjecture.