Conformal type of ends of revolution in space forms of constant sectional curvature (Q258025)

The authors consider the conformal type (parabolicity and non-parabolicity) of complete ends of revolution immersed in simply connected space forms of constant sectional curvature. The main results are contained in Theorems A, B, C, F, and G. As a concrete result we mention the following. Theorem B. Let \(E\) be a complete end of revolution in \(\mathbb{H}^3\). Suppose that the end \(E\) is contained in the upper half-space of \(\mathbb{H}^3\) determined by the \(c\)-cone for some \(c>0\). Then, the end \(E\) is parabolic. The last section deals with several examples of application of the main results.