Minimal Hypersurface of Revolution in Hyperbolic Space Hn

Abstract:

      Let M be a rotational minimal hypersurface in the hyperbolic space Hⁿ. In this paper, we give differential equation of the generating curve γ in the fundamental domain H₊², and obtain the following clossification theorem.Theorem The rotational minimal hypersurfaces in the hyperbolic space Hⁿ muse be hyperplane or generalized catenoids. Moreover, each generalized cat-enoid is bounded between two parallel hyperplanes and is asymptotic them.