3 problems

Let $M^n$, with $n\geq2$, be a closed contact stationary Legendrian submanifold of $\mathbb{S}^{2n+1}$, and let $\mathbf{B}$ be its second fundamental form. The first-gap conjectur…

Let $M^n$, with $n\geq2$, be a closed minimal Legendrian submanifold in $\mathbb{S}^{2n+1}$, and let $\mathbf{B}$ be its second fundamental form. The minimal Legendrian pinching co…

Leung's weak pinching conjecture. If $n$ is odd and $\sigma(W)\leq\frac{n}{n-1}$, then $W$ is homeomorphic to $S^n$.