Uniqueness of hypersurfaces of constant higher order mean curvature in the hyperbolic space (Q6652161)

A result of [\textit{M. P. do Carmo} and \textit{H. B. Lawson jun.}, Duke Math. J. 50, 995--1003 (1983; Zbl 0534.53049)] characterizes horospheres of hyperbolic space as the only complete embedded hypersurfaces with exactly one point in its asymptotic boundary. The authors extend this result to characterize horospheres and equidistant spheres in the class of complete embedded hypersurfaces of hyperbolic space with constant higher order mean curvature functions.