Global properties of constant mean curvature surfaces in \(\mathbb H^2\times\mathbb R\) (Q997137)

The paper discusses some aspects of the global behavior of surfaces of constant mean curvature in \(H^2 \times \mathbb{R}\). A lot of theoretical results were published in this area lately, especially by Meeks, Nelli, Rosenberg, Abresch and Hoffman. The two authors are among the worldwide renowned experts in the area. A very important and interesting maximum principle is presented in this report, for a specific class of H-surfaces. It is a key for mathematician interested in constant mean curvature surfaces.