Complete submanifolds with parallel mean curvature and finite total curvature (Q2735663)

Let \(M\) be a complete noncompact submanifold immersed in a space form of nonpositive sectional curvature, and let \(A\) denote the traceless second fundamental form. The authors prove that if \(M\) has parallel mean curvature vector and finite total curvature, then \(|A|\) goes uniformly to zero at infinity. As applications, they obtain some stability theorems for minimal submanifolds and a rigidity theorem.NEWLINENEWLINEFor the entire collection see [Zbl 0954.00038].