G. Wei

An improved result on Chern conjecture

Let $X: M^n\to \mathbb S^{n+1}(1)$ be a closed minimal hypersurface with constant scalar curvature. Chern conjecture says that a closed minimal hypersurface with constant scalar curvature, $S\geq 2n$ if $S>n$, where $S$ is the squared norm of the second fundamental form. As a partial result, Peng-Terng \cite{pt1, pt2},...