Geodesic
LINEAR WEINGARTEN HYPERSURFACES WITH BOUNDED MEAN CURVATURE IN THE HYPERBOLIC SPACE
Glasgow mathematical journal, Tome 57 (2015) no. 3, pp. 653-663

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DOI

We apply appropriate maximum principles in order to obtain characterization results concerning complete linear Weingarten hypersurfaces with bounded mean curvature in the hyperbolic space. By supposing a suitable restriction on the norm of the traceless part of the second fundamental form, we show that such a hypersurface must be either totally umbilical or isometric to a hyperbolic cylinder, when its scalar curvature is positive, or to a spherical cylinder, when its scalar curvature is negative. Related to the compact case, we also establish a rigidity result. 
AQUINO, CÍCERO P.; LIMA, HENRIQUE F. DE; VELÁSQUEZ, MARCO ANTONIO L. LINEAR WEINGARTEN HYPERSURFACES WITH BOUNDED MEAN CURVATURE IN THE HYPERBOLIC SPACE. Glasgow mathematical journal, Tome 57 (2015) no. 3, pp. 653-663. doi: 10.1017/S0017089514000548
@article{10_1017_S0017089514000548,
     author = {AQUINO, C\'ICERO P. and LIMA, HENRIQUE F. DE and VEL\'ASQUEZ, MARCO ANTONIO L.},
     title = {LINEAR {WEINGARTEN} {HYPERSURFACES} {WITH} {BOUNDED} {MEAN} {CURVATURE} {IN} {THE} {HYPERBOLIC} {SPACE}},
     journal = {Glasgow mathematical journal},
     pages = {653--663},
     year = {2015},
     volume = {57},
     number = {3},
     doi = {10.1017/S0017089514000548},
     url = {http://geodesic.mathdoc.fr/articles/10.1017/S0017089514000548/}
}
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%A LIMA, HENRIQUE F. DE
%A VELÁSQUEZ, MARCO ANTONIO L.
%T LINEAR WEINGARTEN HYPERSURFACES WITH BOUNDED MEAN CURVATURE IN THE HYPERBOLIC SPACE
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%R 10.1017/S0017089514000548
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