Deformations of constant mean curvature-1/2 surfaces in \(\mathbb{H}^2 \times \mathbb{R}\) with vertical ends at infinity (Q2511242)

This paper concerns the theory of CMC surfaces \(H=1/2\) in \(\mathbb{H}^2\times \mathbb{R}\) since this value is critical in the sense that there is no compact CMC surface for \(H\leq 1/2\) while for \(H>1/2\) there are rotational compact examples. A main result is: Theorem 5.14. There exist CMC-\(1/2\) annuli in \(\mathbb{H}^2\times \mathbb{R}\) with vertical ends, that are asymptotic -- regarding the horizontal hyperbolic distance -- to rotational examples with different vertical axis.