Research


Research Interests

My research is included in the field of Geometric Analysis; my interests lie primarily in minimal surfaces, Riemann surfaces, complex geometry, and holomorphic contact geometry.

Most of my main results contribute to the study of minimal surfaces in the Euclidean space Rn by using Complex Analytic tools; in particular, the classical theory of approximation and interpolation for holomorphic mappings and the modern Oka theory. That is the subject of our book with Franc Forstnerič and Francisco J. López entitled Minimal Surfaces from a Complex Analytic Viewpoint, Springer Monographs in Mathematics (2021), Springer International Publishing.

In the last few years I have also studied other topics, such as constant mean curvature one surfaces in the hyperbolic space H3 (also called Bryant surfaces), complex curves in C2, and more generally complex hypersurfaces in the complex Euclidean space Cn, holomorphic null curves in Cn and in the special linear group SL2(C), and holomorphic Legendrian curves in complex contact manifolds.

Research Grants

Together with Joaquín Pérez, we coordinate the research project Geometric Analysis (MTM2017-89677-P and PID2020-117868GB-I00). Also, I am the coordinator of the Spanish Net of Geometric Analysis (RED2018-102361-T).

I am currently engaged in the following research grants.

Geometry Seminar

Together with Miguel Ortega, we coordinate the Geometry Seminar at the Department of Geometry and Topology of the University of Granada. The seminar was established in 1997, and it has been running continuously since then. It covers primarily topics in differential geometry and usually meets on Fridays, during the academic year, at the Math Institute UGR.

The seminar is currently holding in virtual mode due to the Covid-19 pandemic; it will resume its presential activity when the circumstances permit it.

Organization of Events

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