Total squared mean curvature of immersed submanifolds in a negatively curved space

Yanyan Niu, Shicheng Xu

Let $n\ge 2$ and $k\ge 1$ be two integers. Let $M$ be an isometrically immersed closed $n$-submanifold of co-dimension $k$ that is homotopic to a point in a complete manifold $N$,…