Abstract
The main result of this paper states that the traceless second fundamental tensor A0 of an n-dimensional complete hypersurface M, with constant mean curvature H and finite total curvature, ∫M |A0|n dvM < ∞, in a simply-connected space form \(\bar M\)(c), with non-positive curvature c, goes to zero uniformly at infinity. Several corollaries of this result are considered: any such hypersurface has finite index and, in dimension 2, if H 2 + c > 0, any such surface must be compact.
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Bérard, P., do Carmo, M. & Santos, W. Complete Hypersurfaces with Constant Mean Curvature and Finite Total Curvature. Annals of Global Analysis and Geometry 16, 273–290 (1998). https://doi.org/10.1023/A:1006542723958
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DOI: https://doi.org/10.1023/A:1006542723958