We prove that if X : Mn → Hn×R, n≥3, is an orientable, complete immersion with finite strong total curvature, then X is proper and M is diffeomorphic to a compact manifold M minus a finite number of points q1, ... qk. Adding some extra hypothesis, including Hr = 0, where Hr is a higher order mean curvature, we obtain more information about the geometry of a neighbourhood of each puncture. The reader will also find in this paper a classification result for the hypersurfaces of Hn × R which satisfy Hr = 0 and are invariant by hyperbolic translations and a maximum principle in a half-space for these hypersurfaces.

On the structure of hypersurfaces in Hn×R with finite strong total curvature

Nelli, Barbara
2019

Abstract

We prove that if X : Mn → Hn×R, n≥3, is an orientable, complete immersion with finite strong total curvature, then X is proper and M is diffeomorphic to a compact manifold M minus a finite number of points q1, ... qk. Adding some extra hypothesis, including Hr = 0, where Hr is a higher order mean curvature, we obtain more information about the geometry of a neighbourhood of each puncture. The reader will also find in this paper a classification result for the hypersurfaces of Hn × R which satisfy Hr = 0 and are invariant by hyperbolic translations and a maximum principle in a half-space for these hypersurfaces.
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11697/130415
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