The number of conformally equivalent maximal graphs

We show that the number of entire maximal graphs with finitely many singular points that are conformally equivalent is a universal constant that depends only on the number of singularities, namely 2n for graphs with n + 1 singularities. We also give an explicit description of the family of entire maximal graphs with a finite number of singularities all of them lying on a plane orthogonal to the limit normal vector at infinity.Ministerio de Educación y Ciencia MTM2007-64504Junta de Andalucía P06-FQM-01642Junta de Andalucía FQM32

Representación Cartográfica de Datos 3D. Caso práctico.

Este proyecto tiene como objetivo principal poder representar datos 3D en un visor cartográfico, estos datos se encuentran geográficamente referenciados.El proyecto consta dedos partes,la primera trata del tratamiento de los datos lidar y la segunda el desarrollo de un visor. Para finalizar haremos un análisis con las conclusiones del proyecto.This Project has as its main objective represent the 3D data in a map viewer, these data are geographically referenced.This project consists of two parts, the first one is about the treatment of the different lidar data and the second one about the development of a map viewer.To finish we’ll do an analysis of the conclusions of this project

Constant mean curvature surfaces in 3-dimensional Thurston geometries

This is a survey on the global theory of constant mean curvature surfaces in Riemannian homogeneous 3-manifolds. These ambient 3-manifolds include the eight canonical Thurston 3-dimensional geometries, i.e. R3, H3, S3, H2 × R, S2 × R, the Heisenberg space Nil3, the universal cover of PSL2(R) and the Lie group Sol3. We will focus on the problems of classifying compact CMC surfaces and entire CMC graphs in these spaces. A collection of important open problems of the theory is also presented.Ministerio de Educación y Ciencia MTM2007-65249Junta de Andalucía FQM325Junta de Andalucía P06-FQM-0164

Complete minimal surfaces in R3 with a prescribed coordinate function

In this paper we construct complete simply connected minimal surfaces with a prescribed coordinate function. Moreover, we prove that these surfaces are dense in the space of all minimal surfaces with this coordinate function (with the topol- ogy of the smooth convergence on compact sets).Ministerio de Educación y Ciencia MTM2007-61775Ministerio de Educación y Ciencia MTM2007-6450

On the uniqueness of the helicoid and Enneper’s surface in the Lorentz-Minkowski space R31

In this paper we deal with the uniqueness of the Lorentzian helicoid and Enneper’s surface among properly embedded maximal surfaces with lightlike boundary of mirror symmetry in the Lorentz-Minkowski space R3Ministerio de Ciencia y Tecnología MTM2004-00160Ministerio de Ciencia y Tecnología MTM2007-61775Junta de Andalucía P06-FQM-01642Junta de Andalucía FQM32

Totally umbilical disks and applications to surfaces in three-dimensional homogeneous spaces

Following [Ch] and [dCF], we give sufficient conditions for a disk type surface, with piecewise smooth boundary, to be totally umbilical for a given Coddazi pair. As a consequence, we obtain rigidity results for surfaces in space forms and in homogeneous product spaces that generalizes some known results.Ministerio de Educación y Ciencia MTM2007-65249Ministerio de Educación y Ciencia MTM2007-64504Junta de Andalucía P06-FQM-01642Junta de Andalucía FQM32