Related papers: Properly embedded minimal annuli in $\mathbb{H}^2 …

In $\mathbb{S}^2 \times \mathbb{R}$ there is a two-parameter family of properly embedded minimal annuli foliated by circles. In this paper we show that this family contains all properly embedded minimal annuli. We use the description of…

We prove that a minimal oriented stable annular end in H^2 x R whose asymptotic boundary is contained in two vertical lines has finite total curvature and converges to a vertical plane. Furthermore, if the end is embedded then it is a…

In this paper we develop the theory of properly immersed minimal surfaces in the quotient space $\mathbb H^2\times\mathbb R/G,$ where $G$ is a subgroup of isometries generated by a vertical translation and a horizontal isometry in $\mathbb…

For each $k\geq 3$, we construct a 1-parameter family of complete properly Alexandrov-embedded minimal surfaces in the Riemannian product space $\mathbb{H}^2\times\mathbb{R}$ with genus $1$ and $k$ embedded ends asymptotic to vertical…

We prove that a properly embedded annular end of a surface in $\mathbb H^2\times\mathbb R$ with constant mean curvature $0<H\leq \frac{1}{2}$ can not be contained in any horizontal slab. Moreover, we show that a properly embedded surface…

We construct the first examples of complete, properly embedded minimal surfaces in $\mathbb{H}^2 \times \mathbb{R}$ with finite total curvature and positive genus. These are constructed by gluing copies of horizontal catenoids or other…

We construct a one-parameter family of properly embedded minimal annuli in the Heisenberg group Nil_3 endowed with a left-invariant Riemannian metric. These annuli are not rotationally invariant. This family gives a vertical half-space…

We study minimal annuli in $\mathbb{S}^2 \times \mathbb{R}$ of finite type by relating them to harmonic maps $\mathbb{C} \to \mathbb{S}^2$ of finite type. We rephrase an iteration by Pinkall-Sterling in terms of polynomial Killing fields.…

We study constant mean curvature 1/2 surfaces in H2xR that admit a compactification of the mean curvature operator. We show that a particular family of complete entire graphs over H2 admits a structure of infinite dimensional manifold with…

We prove an Alexandrov type theorem for a quotient space of $\mathbb H^2\times \mathbb R$. More precisely we classify the compact embedded surfaces with constant mean curvature in the quotient of $\mathbb H^2\times \mathbb R$ by a subgroup…

We study the existence problem for tilted unduloids in $\mathbb{H}^2\times\mathbb{R}$. These are singly periodic annuli with constant mean curvature $H>1/2$ in $\mathbb{H}^2\times\mathbb{R}$, and the periodicity of these surfaces is with…

Let $\mathbb{M}^{2}$ be a complete non compact orientable surface of non negative curvature. We prove in this paper some theorems involving parabolicity of minimal surfaces in $\mathbb{M}^{2}\times\mathbb{R}$. First, using a…

We classify 'primitive normal compactifications' of C^2 (i.e. normal analytic surfaces containing C^2 for which the curve at infinity is irreducible), compute the moduli space of these surfaces and their groups of auomorphisms. In…

In this paper we prove a general and sharp Asymptotic Theorem for minimal surfaces in $H^2\times R$. As a consequence, we prove that there is no properly immersed minimal surface whose asymptotic boundary $C$ is a Jordan curve homologous to…

We prove that if a complete, properly embedded, finite-topology minimal surface in S^2 x R contains a line, then its ends are asymptotic to helicoids, and that if the surface is an annulus, it must be a helicoid.

We consider compact connected minimal surfaces, with a pair of boundary curves (not necessarily convex) in distinct planes, that have least-area amongst all orientable surfaces with the same boundary. When the planes containing these two…

For any m > 0, we construct properly embedded minimal surfaces in H^2 x R with genus zero, infinitely many vertical planar ends and m limit ends. We also provide examples with an infinite countable number of limit ends. All these examples…

We study closures of GL_2(R)-orbits on the total space of the Hodge bundle over the moduli space of curves under the assumption that they are algebraic manifolds. We show that, in the generic stratum, such manifolds are the whole stratum,…

In this paper we prove that a complete minimal surface immersed in H^2xR, with finite total curvature and two ends, each one asymptotic to a vertical geodesic plane, must be a horizontal catenoid. Moreover, we give a geometric description…

Let H be a semisimple algebaric group and let X be a smooth projective curve defined over an algebraically closed field k. In the first part of this paper we show that the moduli of semistable principal H-bundles exists once given a…