Conformal type of ends of revolution in space forms of constant sectional curvature

In this paper, we consider the conformal type (parabolicity or non-parabolicity) of complete ends of revolution immersed in simply connected space forms of constant sectional curvature. We show that any complete end of revolution in the 3-dimensional Euclidean space or in a 3-dimensional sphere is parabolic. In the case of ends of revolution in the hyperbolic 3-dimensional space, we find sufficient conditions to attain parabolicity for complete ends of revolution using their relative position to the complete flat surfaces of revolution.Work partially supported by the Universitat Jaume I Research Program Project P1-1B2012-18, and DGI-MINECO grant (FEDER) MTM2013-48371-C2-2-P