This survey paper investigates, from a purely geometric point of view, Daniel's isometric
conjugation between minimal and constant mean curvature surfaces immersed in …

We construct the first examples of complete, properly embedded minimal surfaces in ℍ 2× ℝ
with finite total curvature and positive genus. These are constructed by gluing copies of …

Given k≥ 2, we construct a (2k− 2)-parameter family of properly embedded minimal
surfaces in ℍ2× ℝ invariant by a vertical translation T, called saddle towers, which have total …

Laurent Hauswirth and Harold Rosenberg developed in 5 the theory of minimal surfaces
with finite total curvature in \mathbbH^2*\mathbbR. They showed that the total curvature of …

1. Introduction. A properly embedded surface Σ in H 2× R, invariant by a non-trivial discrete
group of isometries of H 2× R, will be called a periodic surface. We will discuss periodic …

We obtain area growth estimates for constant mean curvature graphs in E (κ, τ) E (κ, τ)-
spaces with κ ≤ 0 κ≤ 0, by finding sharp upper bounds for the volume of geodesic balls in E …

We consider the asymptotic behavior of properly embedded minimal surfaces in ℍ2× ℝ,
taking into account the fact that there is more than one natural compactification of this space …

In this paper we prove that a complete minimal surface immersed in H 2 Ũ R, with finite total
curvature and two ends, each one asymptotic to a vertical geodesic plane, must be a …

We show the existence of a-parameter family of properly Alexandrov-embedded surfaces
with constant mean curvature in. They are symmetric with respect to a horizontal slice and …

It is known that a complete immersed minimal surface with finite total curvature in H^ 2 * RH
2× R is proper, has finite topology and each one of its ends is asymptotic to a geodesic …