3 problems

Let $M^n$ be a closed minimal submanifold of the unit sphere $\mathbb S^{n+m}$. With respect to a local orthonormal normal frame, let $\mathcal A$ be the fundamental matrix of the…

Let $M$ be an $n$-dimensional minimal submanifold in $S^{n+m}$. Let $\lambda_2$ denote the quantity used in the paper, and suppose that $||\sigma||^2+\lambda_2$ is constant. Pinchi…

Let $M$ be the submanifold under consideration, let $\sigma$ denote its second fundamental form, and let $n$ be its dimension. Pinching conjecture. There is a constant…