On the compactness of constant mean curvature hypersurfaces with finite total curvature (Q1125395)

This paper is based on the notion of finite total curvature introduced by \textit{P. Bérard, M. do Carmo} and \textit{W. Santos} [Ann. Global Anal. Geom. 16, 273-290 (1998; Zbl 0921.53027)]. The principal result of this paper is the following: {Theorem 1.1.} Let \(M^n\rightarrow Q^{n+1}(c)\) be a complete, orientable \(n\)-manifold immersed in a simply-connected manifold with constant sectional curvature \(c\leqslant 0.\) Assume that \(M\) has parallel mean curvature vector \(h,\) with \(|h|^2 >-c.\) If \(M\) has finite total curvature, then \(M\) must be compact.