Hola, I’m Francisco Torralbo, PhD in Mathematics and assistant professor at the Universidad de Granada. I am the cosupervisor of the research project CMC and member of IMAG.
My research interests include the theory of surfaces of constant mean or constant Gauss curvature, mainly in three and four-dimensional manifolds.
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We study the global geometry of families of tubes of constant mean curvature invariant under screw-motions in homogeneous $\mathbb{E}(\kappa, \tau)$-spaces. In particular, we study embeddedness and prove a foliation result. Moreover, we study numerically the isoperimetric profile in the compact case.
This survey paper investigates, from a purely geometric point of view, Daniel’s isometric conjugation between minimal and constant mean curvature surfaces immersed in homogeneous Riemannian three-manifolds with isometry group of dimension four. On the one hand, we collect the results and strategies in the literature that have been developed so far to deal with the analysis of conjugate surfaces and their embeddedness. On the other hand, we revisit some constructions of constant mean curvature surfaces in the homogeneous product spaces $\mathbb{S}^2\times \mathbb{R}$, $\mathbb{H}^2\times \mathbb{R}$ and $\mathbb{R}^3$ having different topologies and geometric properties depending on the value of the mean curvature. Finally, we also provide some numerical pictures using Surface Evolver.
We survey different classification results for surfaces with parallel mean curvature immersed into some Riemannian homogeneous four-manifolds, including real and complex space forms, and product spaces. We provide a common framework for this problem, with special attention to the existence of holomorphic quadratic differentials on such surfaces. The case of spheres with parallel mean curvature is also explained in detail, as well as the state-of-the-art advances in the general problem.
A relation, via the Gauss map, between the maximal spacelike surfaces in anti De-Sitter space and minimal Lagrangian immersions in the product of two hyperbolic planes is presented. Using this connection new examples of minimal surfaces invariant under the action of one-parameter groups of isometries are constructed.
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During the academic year 2025–2026 I am teaching the following courses:
Toda la información relativa al curso puedes encontrarla en la plataforma PRADO
Toda la información relativa al curso puedes encontrarla en la plataforma PRADO
Toda la información relativa al curso puedes encontrarla en la plataforma PRADO
