Abstract.
In this work we consider a complete submanifold M with parallel mean curvature vector h immersed in a space form of constant sectional curvature \(c\leq 0\). If M has finite total curvature and \(|H|^2>-c\), we prove that M must be compact.
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Received: 3.6.1998
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do Carmo, M., Cheung, LF. & Santos, W. On the compactness of constant mean curvature hypersurfaces with finite total curvature. Arch. Math. 73, 216–222 (1999). https://doi.org/10.1007/PL00000402
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DOI: https://doi.org/10.1007/PL00000402